CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Verify Rolle's theorem for the function $$\displaystyle f(x)=10x-x^{2}$$ in the interval [0,10]


A
Yes Rolle's theorem is applicable and the stationary point is x=5
loader
B
Yes Rolle's theorem is applicable and the stationary point is x=4
loader
C
No Rolle's theorem is not applicable in the given interval
loader
D
none of these
loader

Solution

The correct option is A Yes Rolle's theorem is applicable and the stationary point is $$x=5$$
$$f\left( x \right) =10x-{ x }^{ 2 }\quad \quad \left[ 0,10 \right] $$
$$10x-{ x }^{ 2 }$$ is continuous in $$\left[ 0,10 \right] $$ since it is polynomial function.
$$f'\left( x \right) =10-2x$$ is defined for all values of x in $$(0,10)$$
$$\Rightarrow f\left( x \right) $$ is differentiable  on $$(0,10)$$
$$f\left( 0 \right) =f\left( 10 \right) =0$$
$$\therefore $$ There exists a $$c,a\le c\le b$$
$$0\le c\le 10$$
Such that 
$$f'\left( c \right) =0$$
$$10-2x=0$$
$$x=5$$  $$5$$ lies in $$\left[ 0,10 \right] $$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image