Download App

Differentiability — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiability3 Marks
Question
If $f(x)$ is defined by $f(x) x^2$. find $f(2)$.
✓

Answer

Given: $f(x) = x^2$.
We know a polynomial function is everywhere differentiable. Therefore f(x) is differentiable at $x = 2$.
$\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(2+\text{h})-\text{f}(2)}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(2+\text{h})2-22}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(4+\text{h}2-4\text{h})-4}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{\text{h}(\text{h}+4)}{\text{h}}$
$\Rightarrow\text{f}'(2)=4$

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 Differentiability→Differentiability — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the following differential equations:

$\frac{d y}{d x}+ y \cot x = x ^2 \cot x +2 x$

→
Evaluate the following integrals:
$\int\frac{\text{e}^{2\text{x}}}{1+\text{e}^\text{x}}\text{ dx}$
→
Diffrentiate the following w.r.t.x

$\frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}}$

→
If $4\sin^{-1}\text{x}+\cos^{-1}\text{x}=\pi,$ then what is the value of x?
→
Give examples of two functions f : N → N and g : N → N, such that gof is onto but f is not onto.
→
Evaluate the following integrals:$\int\frac{\log\text{x}}{\text{x}^{\text{n}}}\text{dx}$
→
Evaluate: $\int_0^1 x \cdot \tan ^{-1} x d x$
→
If f : A → B and g : B → C are onto functions, show that gof is a onto function.
→
Evaluate: $\int \frac{x^2}{\left(x^2+2\right)\left(2 x^2+1\right)} d x$
→
A vector $\vec{\text{r}}$ is inclined to x-axis at 45º and y-axis at 60º. If $|\vec{\text{r}}|=8$ units, find $\vec{\text{r}}$.
→