6.

Given f(2) = 25, f'(2) = 7, and f''(x) < 0 for x 2, which one of the following statements about f(6) must be true?

f(6) must be less than -3

f(6) must be greater than -3

f(6) must be less than -10

f(6) must be equal to -24

f(6) must be greater than -24

7. - Curve Sketching Course Packet on inflection points

Consider the function f(x) = 3x5 75x4 + 41x 22.

Enter the number of inflection points of f(x).

Determine the x-coordinates of the inflection 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 inflection points. 8. - Curve Sketching Course Packet on inflection points

Consider the function f(x) = 3x5 40x3 + 17x 42.

Enter the number of inflection points of f(x).

Determine the x-coordinates of the inflection 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 inflection points. 9. - Curve Sketching Course Packet on inflection points

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

WebAssign Plot

Based on the above graph of the second derivative of f(x), determine the number inflection points 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 = 6.

Enter the number of inflection points of f(x):

Determine the x-coordinates of the inflection 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 inflection points. 10. - Curve Sketching Course Packet on points of diminishing & increasing returns

The total monthly revenue R(x) generated from sales of Calculus videos is related to the amount x spent on advertising by

R(x)= 5x3 + 60x2 + 90x + 70

where x is in thousands of dollars. Calculate the point of diminishing returns for advertising costs.

The point of diminishing returns occurs at x = . This means that if more than dollars is spent on advertising, then each additional dollar spent produces a

---Select--- return on investment than the previous dollar.