Honors Pre-Calc



3.1 – 3.3 Review Name: __________________________________

Intro to Calculus

1. Consider the function[pic]

A. Use the limit process to find the derivative [pic]

B. Find the slope of the tangent line at the point (3, 22)

2. Explain the 3 graphical scenarios where f(x) is not differentiable.

1.

2.

3.

Provide examples of the above situations.

1. 2. 3.

3. Find the equation of the tangent line to [pic] at [pic]

4. Differentiate the following.

A. [pic]

B. [pic]

C. [pic]

D. [pic]

5. Use the product rule to differentiate the following.

A. [pic]

B. [pic]

6. Use the quotient rule to differentiate: [pic]

7. Find the derivative using the quotient rule: [pic]

8. Mr. Santos throws a ball up in the air from the top of the building with a velocity of 5m/s at time t=0. The school is 100 meters tall. The position of the ball at any time (t sec) is

Position statement:[pic]

When does the ball reach its maximum height? What is the maximum height?

When does the ball hit the ground? What is the impact velocity of the ball?

9. Determine the point(s) at which the graph of the function has a horizontal tangent line.

A. [pic]

B. [pic]

10. Find the second derivative.

A. [pic]

B. [pic]

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