a. use the definition $m_{tan}=lim_{h \to 0}\frac{f(a + h)-f(a)}{h}$ to find the slope of the line tangent…

a. use the definition $m_{tan}=lim_{h \to 0}\frac{f(a + h)-f(a)}{h}$ to find the slope of the line tangent to the graph of f at p. b. determine an equation of the tangent line at p. f(x)= - 8x + 4, p(2,-12) a. $m_{tan}=square$

a. use the definition $m_{tan}=lim_{h \to 0}\frac{f(a + h)-f(a)}{h}$ to find the slope of the line tangent to the graph of f at p. b. determine an equation of the tangent line at p. f(x)= - 8x + 4, p(2,-12) a. $m_{tan}=square$

Answer

Explanation:

Step1: Identify values of a

Given point $P(2,- 12)$, so $a = 2$. And $f(x)=-8x + 4$.

Step2: Find $f(a + h)$ and $f(a)$

$f(a+h)=-8(a + h)+4=-8a-8h + 4$, when $a = 2$, $f(2 + h)=-8\times2-8h + 4=-16-8h + 4=-12-8h$. $f(a)=f(2)=-8\times2 + 4=-16 + 4=-12$.

Step3: Calculate the slope $m_{tan}$

$m_{tan}=\lim_{h\rightarrow0}\frac{f(a + h)-f(a)}{h}=\lim_{h\rightarrow0}\frac{(-12-8h)-(-12)}{h}=\lim_{h\rightarrow0}\frac{-12-8h + 12}{h}=\lim_{h\rightarrow0}\frac{-8h}{h}$. Cancel out $h$ (since $h\neq0$ when taking the limit), we get $m_{tan}=-8$.

Answer:

$-8$