Question

if f(x)=xn and f'(1)=7,then find the value of n​

Answer 1

Answer:

n = 7

Step-by-step explanation:

Given---> f ( x ) = xⁿ and f¹ ( 1 ) = 7

To find---> Find the value of n

Solution----> We know that ,

d /dx ( xⁿ ) = n xⁿ⁻¹

Now, ATQ,

f ( x ) = xⁿ

Differentiating with respect to x , we get,

f¹ ( x ) = d / dx ( xⁿ )

= n xⁿ⁻¹

Now, f¹ ( 1 ) = n ( 1 )ⁿ⁻¹

Putting f¹ ( 1 ) = 7 , we get,

=> 7 = n ( 1 )ⁿ⁻¹

We know that ( 1 )ᵃ = 1 , using it here , we get,

=> 7 = n ( 1 )

=> 7 = n

=> n = 7