[SOLVED] Use a computer algebra system to find

> (a)Find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.

> Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

> Find the derivative of the trigonometric function.

> The slope of the function Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

> The graphs of f and g are shown. Let h(x) = f (g(x)) and s(x) = g( f (x)). Find each derivative, if it exists. If the derivative does not exist, explain why. Find hâ (1) Find sâ (5)

> Given that g(5) = â3, gâ²(5) = 6, h(5) = 3, and hâ²(5) = â2, find fâ²(5) for each of the following, if possible. If it is not possible, state what additional informati

> The table shows some values of the derivative of an unknown function f. Complete the table by finding the derivative of each transformation of f, if possible. g(x) = f(x) â 2 h(x) = 2 f(x) r(x) = f(-3x) s(x) = f(x + 2)

> Consider the function In general, how do you find the derivative of composite function? Find râ²(x) using the Product Rule. Find râ²(x) using the Quotient Rule. Which method do you prefer? Explain.

> Describe the relationship between f′ and g′. g(x) = f(3x) g(x) = f(x2 )

> The graphs of a function f and its derivative fâ² are shown. Label the graphs as f or fâ² and write a short paragraph stating the criteria you used in making your selection.

> Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result.

> y = (2x - 7)3 Find the derivative of the function.

> Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result.

> f(x) = sec2 πx Find the second derivative of the function.

> Find the second derivative of the function.

> f(x) = 6(x3 + 4)3 Find the second derivative of the function.

> f(x) = 5(2 – 7x)4 Find the second derivative of the function.

> Determine the point(s) at which the graph of has a horizontal tangent.

> Find an equation of the tangent line to the graph at the given point. Then use a graphing utility to graph the function and its tangent line at the point in the same viewing window. Bullet-nose curve

> Complete the table.

> Find an equation of the tangent line to the graph at the given point. Then use a graphing utility to graph the function and its tangent line at the point in the same viewing window. Semicircle

> (a)Find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.

> y = (4x3 + 3)2, (-1, 1) (a)Find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility t

> (a)Find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.

> Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

> Complete the table.

> Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

> Find the slope of the tangent line to the sine function at the origin. Compare this value with the number of complete cycles in the interval [0, 2Ï].

> Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of th

> Complete the table.

> Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of th

> Find the derivative of the trigonometric function.

> y = 5 cos (πt ) 2 Find the derivative of the trigonometric function.

> Complete the table.

> f(t) = 3 sec (πt−1 ) 2 Find the derivative of the trigonometric function.

> Find the derivative of the trigonometric function.

> g(t) = 5 cos 2 πt Find the derivative of the trigonometric function.

> y = 4 sec2 x Find the derivative of the trigonometric function.

> Find the derivative of the trigonometric function.

> y = csc (1 – 2x)2 Find the derivative of the trigonometric function.

> Complete the table.

> Find the derivative of the trigonometric function.

> Find the derivative of the trigonometric function. y = cos 4x

> Find the derivative of the function. g(x) – (2 + (x2 + 1)4)3

> Find the derivative of the function. f(x) = ((x2 + 3)5 + x)2

> Find the derivative of the function.

> Find all differentiable functions f : RâR such that for all real numbers x and all positive integers n

> Prove that d/dx [cos x] = -Sin x.

> Where are the functions f1(x) = ∣sin x∣ and f2(x) = sin ∣x∣ differentiable?

> Find a and b such that f is differentiable everywhere.

> Find the equation(s) of the tangent line(s) to the graph of the parabola y = x2 through the given point not on the graph. (a) (0, a) (b) (a, 0) Are there any restrictions on the constant a?

> Find the equation(s) of the tangent line(s) to the graph of the curve y = x3 − 9x through the point (1, −9) not on the graph.

> Let (a, b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the triangle formed by the tangent line through (a, b) and the coordinate axes is 2.

> Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at (1, 0).

> Find the derivative of the function.

> The annual inventory cost C for a manufacturer is where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 350 to 351 and compare this with the instantaneous rate of change when Q = 350.

> Verify that the average velocity over the time interval [t0 â ât, t0 + ât] is the same as the instantaneous velocity at t = t0 for the position function

> A car is driven 15,000 miles a year and gets x miles per gallon. Assume that the average fuel cost is $3.48 per gallon. Find the annual cost of fuel C as a function of x and use this function to complete the table. Who would benefit more from a one-mile-

> The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the

> The area of a square with sides of length s is given by A = s2. Find the rate of change of the area with respect to s when s = 6 meters.

> The volume of a cube with sides of length s is given by V = s3. Find the rate of change of the volume with respect to s when s = 6 centimeters.

> The graph of the velocity function (see figure) represents the velocity in miles per hour during a 10-minute trip to work. Make a sketch of the corresponding position function.

> The graph of the position function (see figure) represents the distance in miles that a person drives during a 10-minute trip to work. Make a sketch of the corresponding velocity function.

> Use the position function s(t) = −4.9t 2 + v0 t + s0 for free-falling objects. A rock is dropped from the edge of a cliff that is 214 meters above water. (a) Determine the position and velocity functions for the rock. (b) Determine the average velocit

> Use the position function s(t) = −4.9t 2 + v0 t + s0 for free-falling objects. A projectile is shot upward from the surface of Earth with an initial velocity of 120 meters per second. What is its veloc ity after 5 seconds? After 10 seconds?

> Find the derivative of the function.

> Complete the table.

> Use the position function s(t) = −16t 2 + v0 t + s0 for free-falling objects A ball is thrown straight down from the top of a 220-foot building with an initial velocity of −22 feet per second. What is its velocity after 3 seconds? What is its velocity a

> Use the position function s(t) = −16t 2 + v0 t + s0 for free-falling objects. A silver dollar is dropped from the top of a building that is 1362 feet tall. (a) Determine the position and velocity functions for the coin. (b) Determine the average veloc

> Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

> Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(t) = t 2 − 7, [3, 3.1]

Question: Use a computer algebra system to find