Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 2.3

Find all horizontal and vertical tangents to the curve of Example 2.

## Verified Solution

There are vertical tangents when

$f_{1}^{\prime}(t)=6 t^{2}-30 t+24=0=6\left(t^{2}-5 t+4\right)=6(t-4)(t-1)$,

or when t = 1 and t = 4, since $f_{2}^{\prime}(t)$ is nonzero at these points. When t = 1,  x = 18; and when t = 4, x = -9. Thus the vertical tangents are the lines x = 18 and x = -9. There is a horizontal tangent when 2 t + 1 = 0, or $t=-\frac{1}{2}$. When $t=-\frac{1}{2}, y=\frac{3}{4}$; and the line $y=\frac{3}{4}$ is a horizontal tangent.