16. - Curve Sketching Course Packet on critical points

Consider the function f(x) = 4x3 21x2 24x + 9.

Enter the number of critical points/numbers of f(x).

Determine the x-coordinates of the critical points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if f(x) does not have any critical points. 17. - Curve Sketching Course Packet on relative extrema - Curve Sketching Course Packet on critical points

The following graph corresponds to f(x). If the graph does not appear, please reload the page.

WebAssign Plot

Based on the above graph of f(x), determine the number critical points and relative extrema of f(x). You may assume that f(x) is continuous and defined for all x on the interval shown.

Enter the number of critical points/numbers of f(x):

Enter the number of relative maxima of f(x):

Enter the number of relative minima of f(x):

18. - Curve Sketching Course Packet on critical points - Curve Sketching Course Packet on classifying critical points using the first derivative test

The following graph corresponds to f'(x), the first derivative of f(x). If the graph does not appear, please reload the page.

WebAssign Plot

Based on the above graph of the derivative of f(x), determine the number critical points and relative extrema of f(x). You may assume that f'(x) is continuous, f'(x) is defined for all x, and f'(x) = 0 only when x = 7, x = 0, and x = 7.

Enter the number of critical points/numbers of f(x):

Enter the number of relative maxima of f(x):

Enter the number of relative minima of f(x):

19. - Curve Sketching Course Packet on critical points - Curve Sketching Course Packet on classifying critical points using the first derivative test

Determine the x-coordinates of the relative extrema of the function g(x) = 6x5 90x3 + 26.

Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if g(x) does not have any relative maximum or minimum values, respectively.

x-coordinates of the relative maxima = x-coordinates of the relative minima = 20. - Curve Sketching Course Packet on critical points - Curve Sketching Course Packet on classifying critical points using the first derivative test

Determine the x-coordinates of the relative extrema of the function g(x) = x4 8x3 32x2 + 1.

Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if g(x) does not have any relative maximum or minimum values, respectively.

x-coordinates of the relative maxima =

x-coordinates of the relative minima =