if f(x)= -7x² + 3x - 3, find the difference quotient of f, which is given by (f(x + h)-f(x))/h. completely…

Answer:

$-14x - 7h+3$

Explanation:

Step1: Find $f(x + h)$

[ \begin{align*} f(x + h)&=-7(x + h)^2+3(x + h)-3\ &=-7(x^{2}+2xh+h^{2})+3x + 3h-3\ &=-7x^{2}-14xh-7h^{2}+3x + 3h-3 \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(-7x^{2}-14xh-7h^{2}+3x + 3h-3)-(-7x^{2}+3x - 3)\ &=-7x^{2}-14xh-7h^{2}+3x + 3h-3 + 7x^{2}-3x + 3\ &=-14xh-7h^{2}+3h \end{align*} ]

Step3: Find the difference - quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{-14xh-7h^{2}+3h}{h}\ &=\frac{h(-14x - 7h+3)}{h}\ &=-14x - 7h+3 \end{align*} ]