Let f x -sin x 2 -3x -x- 0 6x-5 x 2 -x-0 - Then at x- 0- f x

The correct option is A has a local minimum f(x) = sin(x^2 3x), #160; x≤ 0 #160; #160; #160; #160; #160; #160; = 6x+5x^2, #160; ...

You visited us 16 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

Let f x =si...

Question

Let $f (x) = {\begin{matrix} sin (x^{2} - 3 x), x \leq 0 6 x + 5 x^{2}, x > 0 \end{matrix}$ Then at $x = 0, f (x)$

has a local maximum

No worries! We‘ve got your back. Try BYJU‘S free classes today!

has a local minimum

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

is discontinuous

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A has a local minimum
$f (x) = sin (x^{2} - 3 x), x \leq 0$
$= 6 x + 5 x^{2}, x > 0$
$f^{'} (x) = sin (x^{2} - 3 x) . (2 x - 3), x \leq 0$
$= 6 + 10 x, x > 0$
Although $f (x)$ in not differentiable at $x = 0$ but by looking at the nature
it can be said that in acquire local minima at $x = 0.$

Suggest Corrections

Similar questions

Q. Let

f (x)

be a function defined as below :

f (x) = {\begin{matrix} sin (x^{2} - 3 x), x \leq 0 6 x + 5 x^{2}, x > 0 \end{matrix}

Then at

x = 0, f (x)

Let $f (x) = ⎧ ⎨ ⎩ \begin{matrix} ∣ ∣ x^{2} - 3 x ∣ ∣ + a, 0 \leq x < \frac{3}{2} - 2 x + 3 x \geq \frac{3}{2} \end{matrix}$ If f(x) has a local maximum at x =.

f (x)

is cubic polynomial which has local maximum at

x = - 1

. If

f (2) = 18, f (1) = - 1

and

f (x)

has local minima at

x = 0

, then

f (x)

is cubic polynomial with

f (2) = 18

and

f (1) = - 1.

Also

f (x)

has local maxima at

x = - 1

and

f' (x)

has local minima at

x = 0

, then

Q. Let

f (x) = {\begin{matrix} \begin{matrix} 1 - x + a, & x \leq 1 \end{matrix} \begin{matrix} 2 x + 3, & x > 1 \end{matrix} \end{matrix}

. If

f (x)

has local minimum at

x = 1,

then

a \leq

Join BYJU'S Learning Program

Let f(x)={sin(x2−3x),x≤06x+5x2,x>0 Then at x=0, f(x)

The correct option is A has a local minimumf(x)=sin(x2−3x),x≤0 =6x+5x2,x>0f′(x)=sin(x2−3x).(2x−3),x≤0 =6+10x,x>0Although f(x) in not differentiable at x=0 but by looking at the natureit can be said that in acquire local minima at x=0.

Let $f (x) = {\begin{matrix} sin (x^{2} - 3 x), x \leq 0 6 x + 5 x^{2}, x > 0 \end{matrix}$ Then at $x = 0, f (x)$