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Chapter 2: Q 1. (page 237)
Translate expressions written in Leibniz notation to 鈥減rime鈥� notation, and vice versa.
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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
Use the definition of the derivative to find for each function in Exercises
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.
Suppose f is ant cubic polynomial function prove that coefficients of f a, b, c, d can be expressed in terms of values of f(x) and its derivatives at the point x=2
For each function and interval localid="1648297458718" in Exercises localid="1648297462718" , use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" . Then apply Newton鈥檚 method to approximate that root.
localid="1648297471865"
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