Calculus I (MAT 145) Dr. Day Monday September 25, 2017

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Presentation transcript:

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

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

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

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

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

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

Monday, September 25, 2017 MAT 145

Monday, September 25, 2017 MAT 145

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

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

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

Monday, September 25, 2017 MAT 145

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