Chapter 2: Q. 69 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
Short Answer
The derivative of the function is.
Chapter 2: Q. 69 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
The derivative of the function is.
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Get started for freeThe following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
Think about what you did today and how far north you were from your house or dorm throughout the day. Sketch a graph that represents your distance north from your house or dorm over the course of the day, and explain how the graph reflects what you did today. Then sketch a graph of your velocity.
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
When the bowling ball hits the ground, with
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