Chapter 2: Q 43. (page 237)
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Chapter 2: Q 43. (page 237)
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Use thedefinition of the derivative to prove the power rule holds for positive integers powers
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
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 is first dropped, with
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
28.
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