please clarify. do you mean

this is where f'(x) > 0a. increasing

this is where f'(x) < 0b. decreasing

this is where f''(x) > 0c. concave up

this is where f''(x) < 0d. concave down

extrema occur where the derivative is zero or the original function is undefined.Then find any:

e. local extrema

to classify extrema (if necessary):

it is a local maximum if f'(x) = 0 and f''(x) < 0

it is a local maximum if f'(x) = 0 and f''(x) > 0

inflection points occur where f''(x) = 0. at times further tests are needed. to make sure it is an inflection, make sure that f''(x) changes signs on both sides of x. that is, if it is negative to the left of x and then positive to the right of x, then x is an inflection point.f. inflection points

as i said, i'm not exactly sure what you function is, but it seems you will need the chain rule here.I'm especially having difficulty finding the deriv. of the function and simplifying. Can someone help me solve all the steps??