the expression (f(x + h) - f(x))/h for h ≠ 0 is called the difference quotient. find and simplify the…

the expression (f(x + h) - f(x))/h for h ≠ 0 is called the difference quotient. find and simplify the difference quotient for the following function. f(x)=8x² + 10x + 2 the difference quotient is . (simplify your answer.)

the expression (f(x + h) - f(x))/h for h ≠ 0 is called the difference quotient. find and simplify the difference quotient for the following function. f(x)=8x² + 10x + 2 the difference quotient is . (simplify your answer.)

Answer

Answer:

$16x + 8h+10$

Explanation:

Step1: Find $f(x + h)$

$f(x + h)=8(x + h)^2+10(x + h)+2=8(x^{2}+2xh+h^{2})+10x + 10h+2=8x^{2}+16xh+8h^{2}+10x + 10h+2$

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

$f(x + h)-f(x)=(8x^{2}+16xh+8h^{2}+10x + 10h+2)-(8x^{2}+10x + 2)=16xh+8h^{2}+10h$

Step3: Calculate the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{16xh+8h^{2}+10h}{h}=\frac{h(16x + 8h+10)}{h}=16x + 8h+10$