Questions from General Calculus

Q: Verify that the average velocity over the time interval [t0 −

Verify that the average velocity over the time interval [t0 − ∆t, t0 + ∆t] is the same as the instantaneous velocity at t = t0 for the position fu...

Q: The annual inventory cost C for a manufacturer is /

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 wit...

Q: Find the derivative of the function. /

Find the derivative of the function.

Q: Find an equation of the parabola y = ax2 + bx +

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).

Q: Let (a, b) be an arbitrary point on the

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.

Q: Find the equation(s) of the tangent line(s

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.

Q: Find the equation(s) of the tangent line(s

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?

Q: Find a and b such that f is differentiable everywhere.

Find a and b such that f is differentiable everywhere.

Q: Find a and b such that f is differentiable everywhere.

Find a and b such that f is differentiable everywhere.

Q: Where are the functions f1(x) = ∣sin x

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