Question

if f(x)=x^n and if f'(1)=10 find the value of n

Answer 1

Answer:

plzz se the attachment

Answer 2

The value of n is 10.

Given:

• If $f(x) = {x}^{n}$ and
• if $f(1) = 10$

To find:

• Find the value of n.

Solution:

Formula to be used:

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

Step 1:

Find the derivative of f(x).

$\frac{d}{dx} f(x) = f'(x) = n {x}^{n - 1}...eq1$

Step 2:

Put x= 1 in eq1.

$f'(1) = n( {1)}^{n - 1}$

it is given that f'(1)= 10,

So,

$n.( {1)}^{n - 1} = 10$

or

$n(1) = 10$

or

$\bf n = 10$

Thus,

Value of n is 10.

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