Download App

Mean Value Theorems — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMean Value Theorems3 Marks
Question
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\text{x}^{\frac{2}{3}}\text{ on }[-1,1]$
✓

Answer

Here, $\text{f}(\text{x})=\text{x}^{\frac{2}{3}}\text{ on }[-1,1]$
$\text{f}'(\text{x})=\frac{2}{3\text{x}^{\frac{1}{3}}}$
$\text{f}'(0)=\frac{2}{3(0)^{\frac{1}{3}}}$
$\text{f}'(0)=\infty$
So, f'(x) does not exist at $\text{x}=0\in(-1,1)$
⇒ f(x) is not differentialble in $\text{x}\in(-1,1)$
So, Rolle's theorem is not applicable on f(x) in [-1, 1].

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 Mean Value Theorems→Mean Value Theorems — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the probability of success in a single trial is $0.01.$ How many trials are required in order to have a probability greater than $0.5$ of getting at least one success?
→
Evaluate the following definite integrals:$\int_{0}^\limits{4}\frac{1}{\sqrt{4\text{x}-\text{x}^2}}\text{ dx}$
→
Find the area of the pallallelogram determined by the vectors:$2\hat{\text{i}}$ and $3\hat{\text{j}}$
→
Evaluate the following integrals:
$\int\cot^{\text{n}}\text{cosec}^2\text{x}\text{ dx},\text{ n}\neq-1$
→
Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{\text{a}+\text{x}}{1-\text{ax}}\Big)$
→
Find the Cartesian form of the equation of the plane $\bar{r}=(\hat{i}+\hat{j})+s(\hat{i}-\hat{j}+2 \hat{k})+t(\hat{i}+2 \hat{j}+\hat{k})$
→
In ∆ABC prove the following : $\frac{b-c}{a}=\frac{\tan \frac{B}{2}-\tan \frac{C}{2}}{\tan \frac{B}{2}+\tan \frac{C}{2}}$
→
Diffrentiate the following w.r.t.x

$\left(x^2+4 x+1\right)^3+\left(x^3-5 x-2\right)^4$

→
Find the mean and standard deviation of the following probability distributions:
$\text{x}_\text{i}$
$-5$
$-4$
$1$
$2$
$\text{p}_\text{i}$
$\frac{1}{4}$
$\frac{1}{8}$
$\frac{1}{2}$
$\frac{1}{8}$
→
Differentiate the following functions with respect to x:
$\sin^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big)+\sec^{-1}\Big(\frac{1+\text{x}^2}{1-\text{x}^2}\Big),\text{x}\in\text{R}$
→