Question

Answer the following questions about the function whose derivative is given below. f′(x)=(x−5)^2(x+7)
a. what are the critical points of f?
b. On what intervals is f increasing or decreasing?
c. at what points, if any, does f assume local maximum and minimum values?

Answer 1

critical points at the zeros of the derivative

Answer 2

in this example the derivative changes sign at \(-7\) but not at \(5\) since it is \((x-5)^2\)

Answer 3

a) you find critical points by doing this: f′(x)=0
\[(x-5)^{2}(x+7)=0\]then: x-5=0 or x+7=0
find x, then with those x find both y
(x,y) will be critical points, where function changes from decreasing to increasing and the oposite

Answer 4

how do you find the y's?

Answer 5

y=f(x)