/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 31 Given聽that聽u聽=聽u(t),聽v聽=聽... [FREE SOLUTION] | 91影视

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Chapter 3: Q. 31 (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)=2vu+w

Short Answer

Expert verified

dfdt=vu+wdudt+dwdt+2u+wdvdt

Step by step solution

01

Step 1. Given information

A function,f(t)=2vu+w

02

Step 2. Derivative of given function

Differentiating the given function, we get,

dfdt=2v2u+wdudt+dwdt+2u+wdvdt鈬�dfdt=vu+wdudt+dwdt+2u+wdvdt

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Most popular questions from this chapter

Determine whether or not each function f in Exercises 53鈥�60 satisfies 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)=2x,[a,b]=[0,3]

Use the definitions of increasing and decreasing to argue that f(x)=x4 is decreasing on (鈭�鈭�,0] and increasing on [0,鈭�). Then use derivatives to argue the same thing.

The cost of manufacturing a container for frozen orange juice is C(h)=h2-7.4h+13.7cents, where his the height of the container in inches. Your boss claims that the containers will be the cheapest to make if they are 4inches tall. Use Theorem 3.3 to quickly show that he is wrong.

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].

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=x3+3x2
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