Problem : Find the second derivative of f (x) = x ^{3} .
We begin by computing the first derivative:
f'(x) | = | ||
= | |||
= | 3x ^{2} |
f''(x) | = | ||
= | |||
= | 6x |
Problem : For which value of x is f''(x) = 0 , if f has the following graph?
Problem : Find all functions f (x) such that f''(x) = 0 .
The second derivative being zero means that the slope of the graph of the function is constant for all x . The only graphs for which this is true are the lines, so f (x) = mx + b for some constants m and b .