The figure shown below is the graph of the derivative of some function `y = f'(x)'`.

Then

Options

A. f has local minima at `x = a, b` and a local maximum at `x = c`
B. f has local minima at `x = b, c` and a local maximum at `x = a`
C. f has local minima at `x = c, a` and a local maximum at `x = b`
D. the given figure is insufficient to conclude any thing about the local minima and local maxima of f

Answer

C

Explanation

`f'(a)=f'(b)=f'(c)=0`
`{:(f'(a^(-))lt 0 f'(a^(+))gt0),(f'(c')lt0f'(c^(+))gt0):}]"minima at a & c"'`
`f'(b^(-))gt 0 f'(b^(+))lt0]"max. at b"`.