use the definition m_tan = lim x→a (f(x) - f(a))/(x - a) to find the slope of the line tangent to the graph…
use the definition m_tan = lim x→a (f(x) - f(a))/(x - a) to find the slope of the line tangent to the graph of f at p. f(x)=4x + 6, p(-3,-6) m_tan = □
Answer
Answer:
4
Explanation:
Step1: Identify a and f(a)
Given $P(-3,-6)$, so $a = - 3$ and $f(a)=f(-3)=4\times(-3)+6=-12 + 6=-6$.
Step2: Substitute into the formula
$f(x)=4x + 6$, then $m_{\tan}=\lim_{x\rightarrow - 3}\frac{f(x)-f(-3)}{x-(-3)}=\lim_{x\rightarrow - 3}\frac{(4x + 6)-(-6)}{x + 3}=\lim_{x\rightarrow - 3}\frac{4x+12}{x + 3}$.
Step3: Simplify the expression
$\lim_{x\rightarrow - 3}\frac{4x + 12}{x + 3}=\lim_{x\rightarrow - 3}\frac{4(x + 3)}{x + 3}$.
Step4: Evaluate the limit
Cancel out $x + 3$ (since $x\neq - 3$ when taking the limit), we get $\lim_{x\rightarrow - 3}4=4$.