Question

to find the equation of a line, we need the slope of the line and a point on the line. since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. so we just need to find its slope. the slope of a tangent line to f(x) at x = a can be found using the formula $m_{tan}=lim_{x
ightarrow a}\frac{f(x)-f(a)}{x - a}$. in this situation, the function is f(x)= i and a =

Explanation:

Step1: Identify the point - value

We know the tangent line is at the point $(36,6)$. In the formula for the slope of the tangent line $m_{\tan}=\lim_{x
ightarrow a}\frac{f(x)-f(a)}{x - a}$, the $x$-coordinate of the point on the line gives the value of $a$. So $a = 36$.

Step2: Identify the function

Since the point on the tangent - line is $(36,6)$, and we assume the function is such that $f(36)=6$. A common function for which $f(36) = 6$ is $f(x)=\sqrt{x}$ because $\sqrt{36}=6$.

Answer:

$f(x)=\sqrt{x}$, $a = 36$