If y=f(x) and the function is known to attain a maximum point at x0, then at the point x0a.f’(x0) <0b.f’(x0) >0c.f’’(x0) >0d.f’’(x0) <0

At any x, if first order and second order derivatives of a function f is equal to 0 and greater than 0 respectively, then1 pointx is a local maximum of fx is a local minimum ofx is a stationary pointNone of the above

Consider the function and fill in the spaces below.  By the First derivative test, the function has:a local maximum at the point Answer 1 Question 7, Answer 2 Question 7 and a local minimum at the point

Consider the function:𝑓(𝑥)=𝑥3−3𝑥22−36𝑥Find the relative maximum point on this function.

Suppose function f(x) and its derivative f'(x) is well-defined for all real-valued x. It is known that f(x) has only one stationary point x=1. Moreover, we know that f(x) indeed has a maximal point. Is it correct to conclude that x=1 is the maximal point for f(x)? Question 3 Select one: True False

Estimate the input value(s) where the function has a relative extreme point. Identify each relative extreme as a maximum or minimum, and indicate whether the derivative of the function at that point is zero or does not exist.input value maximumor minimum? derivativex = (smaller value) x = (larger value)