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Chapter 2: Q. 88 (page 199)
Use the definition of the derivative to prove the following special case of the product rule
We proved the special case of product function using the definition of the derivative
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Use the definition of the derivative to find for each function in Exercises 34-59
Prove that if f is any cubic polynomial function then the coefficients of f are completely determined by the values of f(x) and its derivative at x=0 as follows
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil鈥檚 instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
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
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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