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Name _______________________________________________ Period __________ Date __________

Calculus – Week 5 Problem Set (Stds 3.1.2 and 3.1.3)

Due Friday October 7th at 3:30 pm at the latest

1. Find the derivative of the function.

a. [pic] b. [pic]

c. [pic] d. [pic]

e. [pic] f. [pic]

g. [pic] h. [pic]

i. [pic] j. [pic]

2. For [pic] find …

a. [pic] b.[pic] c.[pic]

3. For[pic] find …

a.[pic] b.[pic] c.[pic]

4. For [pic] find…

a. [pic] b. [pic] c. [pic]

4. Find the equations of the tangent line and the normal (perpendicular) line to the graph of the function at the given x-value.

a. [pic] [pic]

Tangent: Normal:

b. [pic] [pic]

Tangent: Normal:

c. [pic] [pic]

Tangent: Normal:

5. Determine the point(s), if any, at which the function has a horizontal tangent line.

a. [pic] b. [pic]

c. [pic] d. [pic]

6. Below is the graph of [pic]. [pic] has a vertical tangent line at [pic] and a horizontal tangent line at [pic]. Determine the x-values where the function is continuous but not differentiable. Justify your answers.

[pic]

7. Below is the graph of [pic]. [pic] has a vertical tangent line at [pic] and a horizontal tangent line at [pic]. Determine the x-values where the function is continuous but not differentiable. Justify your answers.

[pic]

8. Determine the values of a and b such that [pic] is differentiable from [pic]

a.[pic] b. [pic]

c. [pic]

9. Determine whether the statement is true or false. If it is true, justify your answer. If it is false, explain why or give an example that shows it is false.

a. If a function is continuous at a point, then it is differentiable at that point.

b. If a function is differentiable at a point, then it is continuous at that point.

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