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

Quizplus · Accepted Answer

A function is concave upward if its second derivative is positive. The provided second derivative is always positive, therefore the function is concave upward for any x. Option A is incorrect as the function being defined for any value of x does not in itself determine concavity. Option C is also incorrect as the positivity of the first derivative only implies that the function is increasing, not necessarily concave upward.

Show That the Function Is Concave Upward Wherever It