Question

# Let $$f\left( x \right) =\left\{ \begin{matrix} { x }^{ { 3 }/{ 5 } }\quad \quad \quad x\le 1 \\ -{ \left( x-2 \right) }^{ 3 }\quad x>1 \end{matrix} \right.$$then the number of critical points on the graph of the function is

A
1
B
2
C
3
D
4

Solution

## The correct option is C $$3$$$$f\left( x \right) =\left\{ \begin{matrix} { x }^{ { 3 }/{ 5 } }\quad \quad \quad x\le 1 \\ -{\left( x-2 \right) }^{ 3 }\quad x>1 \end{matrix} \right.$$Critical points will at  At $$x=2$$, as$${ f }^{ ' }(x)=0$$ At $$x=0$$, $${ f }^{ ' }(x)$$ is not definedAt $$x=1$$, $${ f }^{ ' }(x)$$ does not exist , therefore its a critical point.Thus, there are three critical points.Hence, option 'C' is correct.Mathematics

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