Asked by hannah
suppose that f is a differentiable function with the derivative f'(x)= (x-1)(x=2)(x+3). Determine the values of x for which the function f is increasing and decreasing
Answers
Answered by
oobleck
If you meant f'(x) = (x-1)(x-+2)(x+3)
since the = symbol is on the + key, then it has zeroes at
x = -3, -2, 1
Clearly, f' < 0 for x < -3 and it changes sign at each of the other two zeroes.
so f(x) is decreasing on (∞,-3) U (-2,1)
and increasing on (-3,-2) U (1,∞)
extra credit: what if f'(x) were (x-1) (x-+2)^2 (x+3)
since the = symbol is on the + key, then it has zeroes at
x = -3, -2, 1
Clearly, f' < 0 for x < -3 and it changes sign at each of the other two zeroes.
so f(x) is decreasing on (∞,-3) U (-2,1)
and increasing on (-3,-2) U (1,∞)
extra credit: what if f'(x) were (x-1) (x-+2)^2 (x+3)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.