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; ...

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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

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has a local minimum

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is discontinuous

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none of these

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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 $x = 0.$

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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

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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 $x = 0, f (x)$