The figure show the graph of the derivative of a continuous

Question

1. Find all critical points and local extremes of each function on the given interval f(x)= x³ - 3x + 5 on the entire real number line .

2. Define A(x) to be the area bounded by the t-axis, the line y = 2t and a vertical line at t = x.

(a) Find a formula for A(x)

(b) Determine A' (x)

3. The figure show the graph of the derivative of a continuous function f.

(a) List the critical numbers of f.

(b) What values of x result in a local maximum?

(c) What values of x result in a local minimum?

4. A function and values of x so that f' (x) = 0 are given. Use the Second Derivative test to Determine whether each point (x, f (x)) is a local maximum, a local Minimum or neither.

h(x) x⁴ - 8x² - 2; x = -2, 0, 2.