Chapter 4 section 3

Excel Companion Chapter 4 Section 3
Return to Table of Contents	Return to Chapter 4 Index
Slopes of Tangent Lines	*Tangents.xls*

Open Tangents.xls and display the sheet six graphs. Print this page.

Match each graph with its corresponding function definition (A) - (F) below.

A	B	C	D	E	F
f(x) = x	f(x) = x²	f(x) = x³			f(x) = e^x

Carefully draw tangent lines at the indicated points (a transparent ruler would be helpful) and complete the unshaded cells in the tangent line table below. Some curves have restrictions on their domain and are not defined at certain points. The reciprocal function is an example of a function that is not defined at x = 0. The square root function is not defined for any negative values of x.

Find approximate values (nearest tenth will suffice) for the slope of the tangent line at the indicated points. If the function is undefined or the slope does not exist at a particular point then write undefined or DNE.

		identity	square	cube	reciprocal	square root	exponential (base e)
		f(x) = x	f(x) = x²	f(x) = x³			f(x) = e^x
approximate slope at x =	-2
approximate slope at x =	0				undefined
approximate slope at x =	1/2	1	1	.8	-.4	.7	1.6
approximate slope at x =	2

Tangent Line Table

Enter your name and ID here:

First name Last name ID

Return to Table of Contents

Return to Chapter 4 Index