Download App

Mean Value Theorems — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMean Value Theorems2 Marks
Question
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$
✓

Answer

The given function $\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3].$

The domain of f is given to be (1, 3).

It is a polynomial function.

Thus, it is everywhere derivable and hence continuous.

But

f(1) = 0 and f(3) = 6

$\Rightarrow\text{f}(3)\neq\text{f}(1)$

Hence, Rolle's theorem is not applicable for the given function.

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 "2 Marks" from Mean Value Theorems→Mean Value Theorems — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the vector equation of a plane which is at a distance of 5 unit from the origin and which is normal to the vector $\hat{\text{i}}-2\hat{\text{j}}-2\hat{\text{k}}$
→
If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y} \end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6 \end{bmatrix},$ write the value of (x + y + z).
→
Find $\frac{d y}{d x}$ if 2x + 3y = sin x
→
Find the value of x from the following: $\begin{bmatrix}2\text{x}-\text{y}&5\\3&\text{y} \end{bmatrix}=\begin{bmatrix}6&5\\3&-2 \end{bmatrix}$
→
For the principal values, evaluate the following:
$\sec^{-1}\big(\sqrt2\big)+2\text{cosec}^{-1}\big(-\sqrt2\big)$
→
Simplify $\cos \theta \left[ \begin{array} { c c } { \cos \theta } & { \sin \theta } \\ { - \sin \theta } & { \cos \theta } \end{array} \right] + \sin \theta \left[ \begin{array} { c c } { \sin \theta } & { - \cos \theta } \\ { \cos \theta } & { \sin \theta } \end{array} \right]$.
→
If |x| < 1 and $\text{y}=1+\text{x}+\text{x}^2+\ .....\ \text{to}\ \infty,$ then find the value of $\frac{\text{dy}}{\text{dx}}.$
→
If $\begin{bmatrix}\text{x}&2\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}=2,$ find x.
→
Evaluate the following:
$\sec^{-1}\Big(\sec\frac{13\pi}{4}\Big)$
→
If f : R → R be defined by f(x) = x4, write f-1(1).
→