Questions from Calculus

Q: Find the slope of the tangent line to the graph of the

Find the slope of the tangent line to the graph of the function at the given point. g(x) = 3/2 x + 1, (-2, -2)

Q: The figure shows the graph of g′. /

The figure shows the graph of g′. a. g’(0) = b. g’(3) = c. What can you conclude about the graph of g knowing that g′(1) = -...

Q: Consider the function f(x) = 1/2 x2

Consider the function f(x) = 1/2 x2. a. Use a graphing utility to graph the function and estimate the values of f′(0), f′( 1/2), f′(1), and f′(2). b. Use your results from part (a) to determine the v...

Q: Consider the function f(x) = 1/3 x3

Consider the function f(x) = 1/3 x3. a. Use a graphing utility to graph the function and estimate the values of f′(0), f′( 1/2), f′(1), f′(2) and f′(3). b. Use your results from part (a) to determine...

Q: Evaluate f (2) and f (2.1)

Evaluate f (2) and f (2.1) and use the results to approximate f′(2). f(x) = x(4 − x)

Q: Evaluate f (2) and f (2.1)

Evaluate f (2) and f (2.1) and use the results to approximate f′(2). f(x) = 1/4x3

Q: Use the alternative form of the derivative to find the derivative at

Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3 + 2x2 + 1, c = −2

Q: Use the alternative form of the derivative to find the derivative at

Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = x2 − x, c = 1

Q: Use the alternative form of the derivative to find the derivative at

Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = √│x│, c = 0

Q: Use the alternative form of the derivative to find the derivative at

Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = 3/x, c = 4