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

9-158.
1. Sketch the distance function d(t) = 3t2. Homework Help ✎

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

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

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

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

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

They are the same.