Question

Assume \[f'(c)=0\] and the second derivative exists at \[c\]. Which condition gives a local minimum?

Options

• \[f''(c)<0\]

• \[f''(c)>0\]

• \[f''(c)=0\]

• \[f'(c)<0\]

Answer 1

Under the Second Derivative Test, a positive second derivative at a critical point gives a local minimum. Hence \[f''(c)>0\] identifies a local minimum.