Question

The graph of a function \(f\) and its derivative \(f'\) are shown. Which is bigger, \(f'\left( { - 1} \right)\) or \(f''\left( 1 \right)\)?

Short answer

The value \(f''\left( 1 \right)\) is bigger.

Step-by-step solution

Differentiability of the Function

The function is having differentiability criteria when the derivative of that function is continuous and has a definite value for all points those are lying within the defined domain of that function.

Find which is bigger.

The given graph is:

Clearly, at\(x = 1\), the value of \(f''\left( 1 \right)\) is higher than the value of \(f'\left( { - 1} \right)\)at \(x = - 1\).

Hence, the value \(f''\left( 1 \right)\) is bigger.