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

Suppose f '' is continuous on (−∞, ∞).(a) If f '(3) = 0 and f ''(3) = −5, what can you say about f ?At x = 3, f has a local maximum.At x = 3, f has a local minimum.    At x = 3, f has neither a maximum nor a minimum.More information is needed to determine if f has a maximum or minimum at x = 3.(b) If f '(4) = 0 and f ''(4) = 0, what can you say about f ?At x = 4, f has a local maximum.At x = 4, f has a local minimum.    At x = 4, f has neither a maximum nor a minimum.More information is needed to determine if f has a maximum or minimum at x = 4.

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

Do we have local maximum/minimum here? If yes, find them.

Use the first derivative test to find the two critical points of the function. First point:(Either of the points can be 𝑥1 or 𝑥2.)𝑥1= Relative Maximum Relative Minimum Neither

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