CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
2
loader
C
3
loader
D
4
loader

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 defined
At $$x=1$$, $${ f }^{ ' }(x)$$ does not exist , therefore its a critical point.
Thus, there are three critical points.
Hence, option 'C' is correct.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image