1. Calculus I (MAT 145) Dr. Day Monday September 25, 2017
Secants Slopes to Tangent Slope: Using Limits (2.7/2.8)
The Definition of Derivative (2.7/2.8)
Uses and Applications of the Derivative (2.8)
Monday, September 25, 2017
MAT 145

2. The value f ’(a) is called:
the derivative of f at x = a,
the instantaneous rate of change of f at x = a,
the slope of f at x = a, and
the slope of the tangent line to f at x = a.
Monday, September 25, 2017
MAT 145

3. The derivative in action!
S(t) represents the distance traveled by some object, where t is in minutes and S is in feet. What is the meaning of S’(12)=100?
Monday, September 25, 2017
MAT 145

4. Here is the graph of the function y = |x|.
Why does the derivative NOT exist at x = 0?
Monday, September 25, 2017
MAT 145

5. Three situations for which a derivative DOES NOT EXIST!
Monday, September 25, 2017
MAT 145

6. For each graphed function, state points at which the function is NOT differentiable. Explain your choices!
Monday, September 25, 2017
MAT 145

7. Monday, September 25, 2017
MAT 145

8. Monday, September 25, 2017
MAT 145

9. Here is the graph of a function f. Use it to sketch the graph of f ’.
Monday, September 25, 2017
MAT 145

10. Match each function, a-d, with its derivative, I-IV.
Monday, September 25, 2017
MAT 145

11. Identify each curve. Explain your choices.
Here are the graphs of four functions. One repre- sents the position of a car as it travels, another represents the velocity of that car, a third repre- sents the acceleration of the car, and a fourth graph represents the jerk for that car.
Identify each curve. Explain your choices.
Monday, September 25, 2017
MAT 145

12. Monday, September 25, 2017
MAT 145