Chapter 2: Q 5. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
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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.
25.
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" .
Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
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
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
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