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Chapter 2: Q 7. (page 237)
Find the derivatives of the function:
The derivative of.
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Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
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.
If Katie walked at miles per hour for minutes and then sprinted at miles an hour for minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie’s position over time and a graph of Dave’s position over time on the same set of axes.
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:
After seconds, with
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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