Determine where the function is concave upward and where it is concave downward.

Question

Determine where the function is concave upward and where it is concave downward. (Round your answers to three decimal places, if necessary. Enter your answer using interval notation. If an answer does not exist, enter DNE.)

f(x) = 10x² + 5x^1/2 + 14

Concave upward:
Concave downward:

Complete the following parts.

(a)    The domain of the function f is 

 

 . (Enter your answer using interval notation.)

(b)    To determine the concavity of the function f, we use the  ---Select--- Increasing and Decreasing Test (IDT) First Derivative Test (FDT) Concavity Test (CT) Second Derivative Test (SDT) Closed Interval Optimal Test (CIOT) Other Kinds of Intervals Optimal Test (OKOT) .

(c)    To determine the concavity of the function f, we need the critical numbers of  ---Select--- f f ' f " .

(d)    To find these critical numbers, we need to find  ---Select--- f ' (x) f '' (x) = 

 

 .

(e)    These critical numbers are as follows. (Round your answer(s) to three decimal places, if necessary. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x = 

 

(f)    Then, we use these critical numbers to construct the sign diagram for  ---Select--- f f ' f " .

Answer 1

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