Chapter 2: Q. 32 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
Short Answer
The derivative of the given function is:
Chapter 2: Q. 32 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
The derivative of the given function is:
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Get started for freeUse the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line that passes through the point and is parallel to the tangent line to at .
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.
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.
23.
A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
Suppose f is a polynomial of degree n and let k be some integer with . Prove that if f(x) is of the form
Then where is the k-th derivative of
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