If both f(x) , & ,g(x) are differentiable functions at x = x_0, t… - Vidyadip

MCQ

If both $f(x)\, \& \,g(x) $ are differentiable functions at $x = x_0$, then the function defined as, $h(x) =$ Maximum $ \{f(x), g(x)\} :$

A
is always differentiable at $x = x_0$
B
is never differentiable at $x = x_0$
✓
is differentiable at $x = x_0$ provided $f(x_0) \ne g(x_0)$
D
cannot be differentiable at $x = x_0$ if $f(x_0) = g(x_0) .$

✓

Answer

Correct option: C.

is differentiable at $x = x_0$ provided $f(x_0) \ne g(x_0)$

c
Consider the graph of $h(x) = max(x, x^2)$ at $x = 0$ and $x = 1$

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 "M.C.Q (1 Marks)" from 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the function $g\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{k\sqrt {x + 1} ,\;\;0 \le x \le 3}\\{mx + 2,\;\;3 < x \le 5}\end{array}} \right.$ is differentiable, then the value of $k + m$ is :

$\int\limits_{\pi /4}^{3\pi /4} {\frac{{dx}}{{1 + \cos x}}} $ is equal to

Let $\mathrm{P}(\alpha, \beta, \gamma)$ be the image of the point $\mathrm{Q}(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the point $(2,5,-1)$. If the area of the triangle $\mathrm{PQR}$ is $\lambda$ and $\lambda^2=14 \mathrm{~K}$, then $\mathrm{K}$ is equal to:

If $f(x) = 3x - 5$, then ${f^{ - 1}}(x)$

The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is

Let $S_n=\sum \limits_{k=1}^n k$, denotes the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it is

$\sin\big[\cot^{-1}\big\{\tan\big(\cos^{-1}\text{x}\big)\big\}\big]$ is equal to:

$\text{x}$
$\sqrt{1-\text{x}^2}$
$\frac{1}{\text{x}}$
$\text{none of these}$

Let $f(x)=2 x+\tan ^{-1} x$ and $g(x)=\log _e\left(\sqrt{1+x^2}+x\right)$, $x \in[0,3]$. Then

Choose the correct answer from the given four options.
Let A and B be two events such that $\text{P}(\text{A})=\frac{3}{8},\text{P}({\text{B}})=\frac{5}{8}$ and $\text{P}(\text{A}\cup\text{B})=\frac{3}{4}.$Then $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)\cdot\text{P}\Big(\frac{\text{A'}}{\text{B}}\Big)$ is equal to:

The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{y}\ \text{g}(\text{x})=\text{g}(\text{x})\ \text{g}'(\text{x})$ is a given function of x, is:

$\text{g}(\text{x})+\log(1+\text{y}+\text{g}(\text{x}))=\text{C}$
$\text{g}(\text{x})+\log(1+\text{y}-\text{g}(\text{x}))=\text{C}$
$\text{g}(\text{x})-\log(1+\text{y}-\text{g}(\text{x}))=\text{C}$
None of these.