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. Is it correct to conclude that x=1 is either a maximum or minimum point for f(x)? Question 2 Select one: True False

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

f(x) = xx has a stationary point at [1]

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.

The following function has only one stationary point. What are its coordinates?

Find the 𝑥-values of both critical points of the following function. Then use the first derivative test to classify each of them as either a relative minimum, relative maximum, or neither.𝑦=−𝑥33−𝑥22+30𝑥−8 Find the first derivative.𝑦′=