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Chapter 2: Q 32. (page 237)
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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.
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.
For each function and interval in Exercises , use the Intermediate Value Theorem to argue that the function must have at least one real root on . Then apply Newton’s method to approximate that root.
localid="1648369345806" .
Prove that if f is a quadratic polynomial function then the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows
Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
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