For Exercise determine whether of the following statement is true or false, and explain why.

If f″(x) > 0 on an interval, the function is increasing on that interval.

Step 1 of 3 :

In this problem, we have to determine whether the statement is true or false and explain why.

Step 2 of 3 :

Second derivative tells us about the point of inflection, extrema and the shape of the curve.

Since a function is increasing if its derivative is positive, its slope is increasing if the derivative of the slope function is positive.

Since the derivative of a derivative is the second derivative, it can be used to tell only for slope is increasing or decreasing.