Show that the function is concave upward wherever it is defined.
A) The function is defined for any value of x and hence the function is concave upward for any x.
B) The second derivative of is . It is positive for any value of x, hence the function is concave upward for any x.
C) The first derivative of is . It is positive for any value of x, hence the function is concave upward for any x.

Question

Show that the function  is concave upward wherever it is defined. ​
A) The function is defined for any value of x and hence the function is concave upward for any x. 
B) The second derivative of is . It is positive for any value of x, hence the function is concave upward for any x. 
C) The first derivative of is . It is positive for any value of x, hence the function is concave upward for any x.

Quizplus · Accepted Answer

To show that a function is concave upward, we need to show that its second derivative is positive for all values of x. In choice B, we are given that the second derivative of the given function is always positive, hence the function is concave upward for all values of x. Choices A and C are not necessarily true and do not provide enough information to show that the function is concave upward for all values of x.

Show That the Function Is Concave Upward Wherever It