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

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)=7x² + 9x + 6 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)=7x² + 9x + 6 the difference quotient is . (simplify your answer.)

Answer

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x): [ \begin{align*} f(x + h)&=7(x + h)^2+9(x + h)+6\ &=7(x^{2}+2xh+h^{2})+9x + 9h+6\ &=7x^{2}+14xh+7h^{2}+9x + 9h+6 \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(7x^{2}+14xh+7h^{2}+9x + 9h+6)-(7x^{2}+9x + 6)\ &=7x^{2}+14xh+7h^{2}+9x + 9h+6 - 7x^{2}-9x - 6\ &=14xh+7h^{2}+9h \end{align*} ]

Step3: Find the difference quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{14xh+7h^{2}+9h}{h}\ &=\frac{h(14x + 7h+9)}{h}\ &=14x+7h + 9 \end{align*} ]

Answer:

$14x+7h + 9$