For the function f(x)= x^2+8x, how do you find and simplify f(x+h)-f(x)?

Marin Mills

Marin Mills

Answered question

2023-03-18

For the function f ( x ) = x 2 + 8 x , how do you find and simplify f ( x + h ) f ( x ) ?

Answer & Explanation

ew6indynz9

ew6indynz9

Beginner2023-03-19Added 7 answers

f ( x ) = x 2 + 8 x for variable unknown x
If the variable unknown is x + h then the function f will become:
f ( x + h ) = ( x + h ) 2 + 8 ( x + h )
Thus, f ( x + h ) - f ( x ) is:
[ ( x + h ) 2 + 8 ( x + h ) ] - [ x 2 + 8 x ]
[ ( x + h ) ( x + h ) + 8 x + 8 h ] - x 2 - 8 x
[ x 2 + 2 x h + h 2 ] - x 2 - 8 x
Cancel out any corresponding terms:
x 2 + 2 x h + h 2 - x 2 - 8 x h 2 + 2 x h - 8 x

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