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(C) From the given graph of $f'(x)$,we observe the points where $f'(x) = 0$ are $x=a, b, c$.$1$. At $x=a$: The derivative $f'(x)$ changes sign from ne

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$f$ has local minima at $x=a, c$ and a local maximum at $x=b$

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(C) From the given graph of $f'(x)$,we observe the points where $f'(x) = 0$ are $x=a, b, c$.$1$. At $x=a$: The derivative $f'(x)$ changes sign from negative to positive (as it crosses the x-axis from below to above). Thus,$f(x)$ has a local minimum at $x=a$.$2$. At $x=b$: The derivative $f'(x)$ changes sign from positive to negative (as it crosses the x-axis from above to below). Thus,$f(x)$ has a local maximum at $x=b$.$3$. At $x=c$: The derivative $f'(x)$ changes sign from negative to positive (as it crosses the x-axis from below to above). Thus,$f(x)$ has a local minimum at $x=c$.Therefore,$f(x)$ has local minima at $x=a, c$ and a local maximum at $x=b$. The correct option is $C$.

The figure shown below is the graph of the derivative of some function $y=f(x)$. Then,

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