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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{ - \,\pi /2}^{\,\pi /2} {\,\frac{{\sin x}}{{1 + {{\cos }^2}x}}{e^{ - {{\cos }^2}x}}dx} $ is equal to

If $\int_{\pi /2}^x {\sqrt {3 - 2{{\sin }^2}u} } \,du + \int_0^y {\cos t\,dt} = 0,$ then $\frac{{dy}}{{dx}} = $

If $y(x)$ is the solution of the differential equation

$x d y-\left(y^2-4 y\right) d x=0 \text { for } x>0, y(1)=2 \text {, }$

and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is . . . .

${d \over {dx}}\log |x|{\rm{ }} = ......,(x \ne 0)$

The area enclosed between the curves $y = {x^3}$ and $y = \sqrt x $ is, (in square units)

The function $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$ is

$a=i+j+k,\,b=2i-4k,\,c=i+\lambda \,j+3k$ are coplanar, then the value of $\lambda $ is

A wire of length $36\, \mathrm{~m}$ is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is $\mathrm{k}$ $(meter),$ then $\left(\frac{4}{\pi}+1\right) \mathrm{k}$ is equal to ..... .

If $f(x) = \cos (\log x)$, then the value of $f(x).f(4) - \frac{1}{2}\left[ {f\left( {\frac{x}{4}} \right) + f(4x)} \right]$

The position of a point in time $ ‘ t’ $ is given by $x = a + bt - c{t^2}$, $y = at + b{t^2}$. Its acceleration at time $ ‘t’$ is