Question

Find and simplify the following for f(x)= x(21-x), assuming h#0 in (C). (A) f(x +h) (B) f(x+h) – f(x) (C) f(x+h) – f(x) (D) f(x+h)=

Answer 1

A

`f(x + h) = 21x -x^2 -2xh+ 21h+h^2`

B

`f(x-h)-f(x) = 21h+h^2 -2xh`

C

`(f(x-h)-f(x))/(h) = 21+h -2x`

Explanation:

From the question we are told that

The equation given is

`f(x) = x (21 - x )`

Considering A

`f(x + h) = (x + h) (21 - (x + h))`

`f(x + h) = (x + h) (21 - x - h)`

`f(x + h) = 21x -x^2 -2xh+ 21h+h^2`

Considering B

`f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -[ x(21 -x)]`

`f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -21x + x^2`

`f(x-h)-f(x) = 21h+h^2 -2xh`

Considering C

`(f(x-h)-f(x))/(h) = (21h+h^2 -2xh)/(h)`

`(f(x-h)-f(x))/(h) = (h(21+h -2x))/(h)`

`(f(x-h)-f(x))/(h) = 21+h -2x`