Find the difference quotient of f(x)=8x-x^2

Answer 1

Find the difference quotient of f(x)=8x-x^2

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Consider the difference quotient formula.

f(x+h)−f(x) / h

Replace the variable x with  x+h in the expression

f(x+h) = 8(x+h) -(x+h)²

= 8x+8h-(x² + 2hx +h² )

= 8x +8h -x² -2hx -h²

f (x) = 8x - x²

so substituting value in difference quotient formula

8x +8h -x² -2hx -h² - (8x-x² ) / h

= 8x +8h -x² -2hx -h² -8x +x² / h

= 8h -2hx /h

=h(8-2x) / h

=8-2x