Question

If fx)= alpha x^n prove that alpha=f'(1)/n.​

Answer 1

Answer:

α = f' ( 1 ) / n [ Proved ]

Step-by-step explanation:

Given :

f ( x ) = α xⁿ

We have to prove :

α = f' ( 1 ) / n

Diff. w.r.t. x

Apply power rule here :

f' (  x ) = n α  xⁿ⁻¹

Now f' ( 1 ) :

⇒ f' ( 1 ) = n α 1ⁿ⁻¹

Since there is 1ˣ , so we will get 1 only .

= > f' ( 1 ) = n  α

Rewrite as :

= >  α = f' ( 1 ) / n

Hence proved .