Question

find value of a if 1st differentiation of the function f(x) is 0 at x=0. Where f(x)=x^2-6ax+18?

Answer 1

The value of a = 0

Given :

1st differentiation of the function f(x) is 0 at x = 0. Where f(x) = x² - 6ax + 18

To find :

The value of a

Solution :

Step 1 of 3 :

Write down the given function

Here the given function is

f(x) = x² - 6ax + 18

Step 2 of 3 :

Find 1st differentiation of the function f(x)

f(x) = x² - 6ax + 18

Differentiating both sides with respect to x we get

$\displaystyle \sf{ f'(x) = \frac{d}{dx}( {x}^{2} - 6ax + 18)}$

$\displaystyle \sf{ \implies f'(x) = \frac{d}{dx}( {x}^{2} ) -\frac{d}{dx}( 6ax) +\frac{d}{dx}( 18)}$

$\displaystyle \sf{ \implies f'(x) = \frac{d}{dx}( {x}^{2} ) -6a\frac{d}{dx}( x) +\frac{d}{dx}( 18)}$

$\displaystyle \sf{ \implies f'(x) = 2 \times {x}^{2 - 1} - 6a \times {x}^{1 - 1} + 0 }\: \: \: \bigg[ \: \because \: \frac{d}{dx}( {x}^{n} ) = n {x}^{n - 1} \bigg]$

$\displaystyle \sf{ \implies f'(x) =2x - 6a}$

Step 3 of 3 :

Find the value of a

Here it is given that 1st differentiation of the function f(x) is 0 at x = 0

∴ f'(0) = 0

⇒ 2 × 0 - 6a = 0

⇒ 0 - 6a = 0

⇒ - 6a = 0

⇒ a = 0

Hence the required value of a = 0

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ write the expression for gradient and divergence

https://brainly.in/question/32412615

2. prove that the curl of the gradient of

(scalar function) is zero

https://brainly.in/question/19412715

#SPJ3

Answer 2

Concept: Differentiation is the process of finding the differentiate of a function. Differentiate means that  the rate of change of function.

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

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

Given: f'(x)=0 x=0

Find: Find the value of a in the function.

Solution: $f(x)=x^{2} -6ax+18$

$f'(x)=\frac{d}{dx} (x^{2} -6ax+18)$

$f'(x)=\frac{d}{dx}(x^{2} )-6a\frac{d}{dx} (x)+\frac{d}{dx} (18)$

$f'(x)=2x-6a+0$

$f'(x)=2x-6a$

$f'(x)=0$ (given)

∴ 2x-6a=0  

x=0 (given)

2×0-6a=0

a=0

Final answer: The value of a is 0.

#SPJ3