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Chapter 2: Q. 11 (page 197)

Given that f,g,h are functions with values f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1 Calculate

(3f+4h)'(2)

Short Answer

Expert verified

The value is(3f+4h)'(2)=5

Step by step solution

01

Given information

We are given f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1

02

Compute the given values

We have to find (3f+4h)'(2)

Which can be simplified as

3f'(2)+4h'(2)3(3)+4(-1)9-4=5

Hence the value is(3f+4h)'(2)=5

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x(3x2+1)9

Use the definition of the derivative to find f'for each function fin Exercises 39-54

role="math" localid="1648290170541" f(x)=x-1x+3

The following reciprocal rules tells us hoe to differentiate the reciprocal of a function

ddx(1f(x))=-1[f(x)]2

Prove this using

a) definition of the derivative

b) by using the quotient rule

Velocity v(t) is the derivative of position s(t). It is also true that acceleration a(t) (the rate of change of velocity) is the derivative of velocity. If a race car鈥檚 position in miles t hours after the start of a race is given by the function s(t), what are the units of s(1.2)? What are the units and real-world interpretation of v(1.2)? What are the units and real-world interpretations of a(1.2)?

State the chain rule for differentiating a composition g(h(x))of two functions expressed

(a) in 鈥減rime鈥� notation and

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