### Home > PC > Chapter 9 > Lesson 9.3.5 > Problem9-158

9-158.

Sketch the distance function $d\left(t\right) = 3t^{2}$.

1. Find the slope of the tangent line at $t = 3$.

$\lim\limits_{ h \to 0} \frac{f(3+h)-f(3)}{3+h-3}=\lim\limits_{ h \to 0} \frac{3(3+h)^2-3(3^2)}{h}=?$

2. Find the slope of the tangent line at any point $t$.

$\lim\limits_{ h \to 0} \frac{f(t+h)-f(t)}{t+h-t}=\lim\limits_{ h \to 0} \frac{3(t+h)^-3t^2}{h}=?$

3. How is the expression in part (b) related to the function in problem 9-157?

They are the same.