Question

If y= 3x³ - 9x, for what value of x, dy/dx =0

options
1. x=+1
2.x=-1
3.x=0
4. x=+-1
please answer fast​

Answer 1

GIVEN :–

• A function y = 3x³ - 9x.

• dy/dx = 0

TO FIND :–

• Value of x = ?

SOLUTION :–

$\\ \: \: { \bold{y = 3 {x}^{3} - 9x }} \: \:$

• Using formula –

$\\ \: \: {\huge{.}} \: \: { \bold{\dfrac{d({x}^{n})}{dx} = n {x}^{n - 1} }} \: \:$

• So that –

$\\ \implies{ \bold{ \dfrac{dy}{dx} = 3 (3){x}^{2} - 9 }} \: \:$

$\\ \implies{ \bold{ \dfrac{dy}{dx} = 9{x}^{2} - 9 }} \: \:$

$\\ \: \: { \bold{ \because \: \: \dfrac{dy}{dx} = 0 }} \: \:$

$\\ \: \: { \bold{ \therefore \: \: 9{x}^{2} - 9 = 0 }} \: \:$

$\\ { \bold{ \implies 9({x}^{2} - 1) = 0 }} \: \:$

$\\ { \bold{ \implies {x}^{2} - 1 = 0 }} \: \:$

$\\ { \bold{ \implies {x}^{2} = 1}} \: \:$

$\\ { \bold{ \implies x = \pm \sqrt{1}}} \: \:$

$\\ \implies \large{ \boxed { \bold{x = \pm \: 1}}} \: \:$

● Hence, Option (4) is correct.

Answer 2

question:

⟹ If y= 3x³ - 9x, for what value of x, dy/dx =0

Answer:

option (d) x=±1

Formula used:

$\frac{d {(x)}^{n} }{dx} = n {x}^{n - 1}$

Solution:

dy/dx=3(3)x²-9

dy/dx=9x²-9

dy/dx=0

⟹ 9x²-9=0

⟹ x²-1=0

⟹ x=±√1 (1²=1)

⟹ x=±1