For the above quartic polynomial f( x ) = x 4 /2 + 2 x 3 − 15.75 x 2 , identify the interval on which f is concave down. < x <

Question

For the above quartic polynomial f( x ) = x4/2+2x3−15.75x2, identify the interval on which f is concave down. < x < 

Answer 1

The function is concave downward when the second derivative is negative. You can determine the critical points where the second derivative changes from positive to negative or vice versa by determining where the second derivative is equal to zero. Then pick a point in each of the intervals you identified (before and after the critical points) to determine whether the second derivative is positive or negative.