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 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 equation below. (If an answer does not exist, enter DNE.)f(x) = e9x + e−x(a)Find the interval on which f is increasing. (Enter your answer using interval notation.)(−ln(3)5​,∞) Find the interval on which f is decreasing. (Enter your answer using interval notation.)(−∞,−ln(3)5​) (b)Find the local minimum and maximum values of f.local minimum value −ln(9)10​ local maximum value DNE (c)Find the inflection point.(x, y) =  DNE Find the interval on which f is concave up. (Enter your answer using interval notation.)(−∞,∞) Find the interval on which f is concave down. (Enter your answer using interval notation.

Suppose that 4 ≤ f ′(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) − f(3)? ≤ f(6) − f(3)

How do you determine where f is increasing or decreasing?If f  ′(x) 0 on an interval, then f is increasing on that interval.If f  ′(x) 0 on an interval, then f is decreasing on that interval.

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