Chapter 2: Q. 37 (page 184)
Use (a) the h→0 definition of the derivative and then (b) the z→c definition of the derivative to find f'(c) for each function f and value x = c.
Short Answer
(a)
(b)
Chapter 2: Q. 37 (page 184)
Use (a) the h→0 definition of the derivative and then (b) the z→c definition of the derivative to find f'(c) for each function f and value x = c.
(a)
(b)
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Get started for freeUse (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.
24.
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.
Write down a rule for differentiating a composition of four functions
(a) in “prime” notation and
(b) in Leibniz notation.
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’s method to approximate that root.
localid="1648297471865"
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
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