Verify Rolle’s theorem for the following functions. f(x)= (x 2 ),… - Vidyadip

Question

Verify Rolle’s theorem for the following functions.

$f(x)=\sin \left(\frac{x}{2}\right), x \in[0,2 \pi]$

✓

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Applications of Derivatives→Applications of Derivatives — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Differentiate 3x w.r.t. $\log_{x_ 3. }$

Evaluate the following determinant:
$\begin{vmatrix}\cos15^\circ&\sin15^\circ\\\sin75^\circ&\cos75^\circ \end{vmatrix}$

Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.

Find the length of the perpendicular from the point $(3,2,1)$ to the line $\frac{x-7}{-2}=\frac{y-7}{2}=\frac{z-6}{3} \quad$

Prove that
$\tan^{-1}\Big(\frac{1-\text{x}^2}{2\text{x}}\Big)+\cot^{-1}\Big(\frac{1-\text{x}^2}{2\text{x}}\Big)=\frac{\pi}{2}$

Evaluate the following integrals:
$\int\text{x}^3\sin\text{x}^4\text{dx}$

Integrate the following functions w.r.t x:

$\sin ^5 x \cos ^8 x$

Find the area of the parallelogram whose diagonals are:
$2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}}$ and $3\hat{\text{i}}-6\hat{\text{i}}+2\hat{\text{k}}$

Evaluate the following integrals:
$\int\log(\text{x}+1)\text{dx}$

Diffrentiate the following w.r.t.x

$\log \left[\frac{a^{\cos x}}{\left(x^2-3\right)^3 \log x}\right]$