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Chapter 2: Q 34 (page 238)
Find a function f that has the given derivative and value f(c).
The anti derivative is
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Stuart left his house at noon and walked north on Pine Street for minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart鈥檚 house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist鈥檚 office. When he got there, he found the office closed for lunch; he was minutes early for his appointment. Stuart waited at the office for minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart鈥檚 position over time. Then sketch a graph that describes Stuart鈥檚 velocity over time.
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.
Differentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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