find the difference quotient of f; that is, find (f(x + h) - f(x))/h, h ≠ 0, for the following function…

find the difference quotient of f; that is, find (f(x + h) - f(x))/h, h ≠ 0, for the following function. f(x)= - 8x + 3 (f(x + h) - f(x))/h = (simplify your answer.)

find the difference quotient of f; that is, find (f(x + h) - f(x))/h, h ≠ 0, for the following function. f(x)= - 8x + 3 (f(x + h) - f(x))/h = (simplify your answer.)

Answer

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x): $f(x + h)=-8(x + h)+3=-8x-8h + 3$

Step2: Calculate f(x + h) - f(x)

$f(x + h)-f(x)=(-8x-8h + 3)-(-8x + 3)$ $=-8x-8h + 3 + 8x-3=-8h$

Step3: Calculate the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-8h}{h}$ Since $h\neq0$, we can cancel out h: $\frac{-8h}{h}=-8$

Answer:

$-8$