Download Unit 2 Quiz 1 Review: Derivatives and Tangent Lines and more Exams Mathematics in PDF only on Docsity!
Name: ______________________
Unit 2 Quiz 1 Review Topics
Average rate of change
Slope at a point (I will give the formula for finding it using a limit)
Tangent lines and normal lines
Limit definition of the derivative
Derivative graphs
Differentiability
Power Rule
1. Find the average rate of change of
2 f x x 1 on the interval [1,2].
2. State the limit definition for the derivative of f x .
3. Find the derivative of
f x x
using the limit definition of the derivative.
- Use
0
lim h
f a h f a m h
to find the slope of the line tangent to
2 f x x 1 at x = 3.
- Use the result from the previous problem to find
a. the equation of the tangent line to
2 f x x 1 at x = 3.
b. the equation of the line normal to
2 (^) f x x 1 at x = 3.
6. Explain in your own words what a derivative of a function f x is.
- Is f ( x ) differentiable at x = 2? Explain your answer thoroughly.
-1 1 2 3
1
2
x
y
f x
- Match the graph of the function (top row) with the graph of its derivative (bottom row).
The same scale is used for all graphs.
a) _____ b) _____ c) _____ d) _____
- Match the graph of the function (top row) with the graph of its derivative (bottom row). The same scale is used for all graphs.
a) _____ b) _____ c) _____ d) _____
a b c d
a b c d
