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Chapter 3: Q. 27 (page 299)

Giventhatu=u(t),v=v(t),andw=w(t)arefunctionsoftandthatkisaconstant,calculatethederivativeofeachfunctionf(t)inExercises27鈥�36.Youranswersmayinvolveu,v,w,dudt,dvdt,dwdt,k,and/ort.f(t)=u2+kv

Short Answer

Expert verified

dfdt=2ududt+kdvdt

Step by step solution

01

Step 1. Given information

A function,f(t)=u2+kv

02

Step 2. Derivative of given function

Differentiating the given function, we get,

dfdt=2ududt+kdvdt

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Most popular questions from this chapter

Explain the difference between two antiderivatives of the function.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=2x-15

Determine whether or not each function fsatisfies the hypotheses of the Mean Value Theorem on the given interval [a,b]. For those that do, use derivatives and algebra to find the exact values of all c鈭�(a,b)that satisfy the conclusion of the Mean Value Theorem.

f(x)=sinx,[a,b]=[0,蟺2].

For the graph of f in the given figure, approximate all the values x 鈭� (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.

It took Alina half an hour to drive to the grocery store that is 20 miles from her house.

(a) Use the Mean Value Theorem to show that, at some point during her trip, Alina must have been traveling exactly 40 miles per hour.

(b) Why does what you have shown in part (a) make sense in real-world terms?
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