Reference no: EM13918562
1. Find all of the critical points and local maximums and minimums of the function:
f (x) = x3 - 6x2 + 5
2. Find all critical points and local extremes of the function on the given interval:
f (x) = x5 - 5x4 + 5x3 + 7 on [0, 2]
3. Find the coordinates of the point in the first quadrant on the ellipse 9x2 + 16y2 = 144 so that the rectangle in the figure below has:
(a) the largest possible area.
(b) the smallest possible area.
4. Verify that the hypotheses of the Mean Value Theorem are satisfied for the functions on the given intervals, and find the number( s) "c" that the Mean Value Theorem guarantees:
(a) f (x) = sin(x) on [0, π/2 ]
(b) f (x) = x3 on [-1, 3]
5. Determine a formula for g(x) if you know:
g"(x) = 12x, g'(1) = 9 and g(2) = 30.
6. Sketch the graph of the derivative of the function:
7. Use information from the derivative of the function to help you graph the function. Find all local maximums and minimums of the function:
g(x) = 2x3 - 15x2 + 6
8. The figure below shows the graph of the derivative of a continuous function g.
(a) List the critical numbers of g.
(b) What values of x result in a local maximum?
(c) What values of x result in a local minimum?
9. A function and values of x so that f 0(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.
f (x) = 2x3 - 15x2 + 6; x = 0, 5
10. At which values of x labeled in the figure below is the point (x, g(x)) an inflection point?
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