Chapter 2: Q. 65 (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. 65 (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 freeA 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
In Exercises 69–80, determine whether or not is continuous and/or differentiable at the given value of . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
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Use the limit just defined to calculate the exact slope of the tangent line toat
Use the definition of the derivative to find for each function in Exercises
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.
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