Suppose the derivative of following

Question

Suppose the derivative of f is (x+4)^2 (x-3)^5 (x-5)^4

a)find the intervals on which f is increasing and decreasing.

b) find the x-coordinates of the local minimum values of f .

c) find the x-coordinates of the local maximum values of f .

Thank you!

Answer 1

Hi Justin,

f is increasing where the derivative is positive and decreasing where it is negative.

Local minimums are found at coordinates where the first derivative changes sign from negative to positive.

Local maximums are found where the derivative changes from positive to negative.

Since you've been given the derivative, there's really no calculus left to be done - just use techniques you learned in algebra to do the analysis.