The devariate of a functions of f at x is given by f'(x)=lim_(h->0)(f(x+h)-f(h))/(h) Use the definition of the derivative to find the derivative of f(x)=8x^2+9x+1 Enter the fully simplified expression for f(x+h)-f(x).

koraby2bc

koraby2bc

Answered question

2022-09-26

The devariate of a functions of f at x is given by
f ( x ) = lim h 0 f ( x + h ) f ( x ) h
provide the limit exists
Use the definition of the derivative to find the derivative of f ( x ) = 8 x 2 + 9 x + 1.Enter the fully simplified expression for f(x+h)-f(x).

Answer & Explanation

Abdiel Nelson

Abdiel Nelson

Beginner2022-09-27Added 6 answers

Given: f ( x ) = 8 x 2 + 9 x + 1
Now, f ( x + h ) = 8 ( x + h ) 2 + 9 ( x + h ) + 1 = 8 [ x 2 + h 2 + 2 h x ] + 9 x + 9 h + 1 = 8 x 2 + 8 h 2 + 16 h x + 9 x + 9 h + 1
Now f ( x + h ) = f ( x )
=> [ 8 x 2 + 8 h 2 + 16 h x + 9 x + 9 h + 1 ] [ 8 x 2 + 9 x + 1 ] => 8 h 2 + 16 h x + 9 h
Now, f ( x ) = lim h 0 f ( x + h ) f ( h ) h = lim h 0 8 h 2 + 16 h x + 9 h h = lim h 0 8 h 2 h + lim h 0 16 h x x + lim h 0 9 h h = lim h 0 8 h + lim h 0 16 x + lim h 0 9 = 0 + 16 x + 9 => 16 x + 9

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?