   Chapter 10.6, Problem 31E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 29-38, compute the indicated derivative. U ( t ) = 5.1 t 2 + 5.1 ; U ′ ( 3 )

To determine

To calculate: The value of the derivative U(3) for the function U(t)=5.1t2+5.1.

Explanation

Given Information:

The provided function is U(t)=5.1t2+5.1.

Formula used:

The difference quotient formula is used which is as follows:

f(a)=limh0f(a+h)f(a)h

The square of the sum formula,

(a+b)2=a2+b2+2ab

Calculation:

Consider the function, U(t)=5.1t2+5.1

The difference quotient formula used to estimate the exact value of derivative algebraically is:

f(a)=limh0f(a+h)f(a)h

But, according to the question,

U(a)=limh0U(a+h)U(a)h

Substitute a=3 into the above formula,

U(3)=limh0U(3+h)U(3)h

Here U(3)=5.1(3)2+5.1 then,

U(3+h)=5.1(3+h)2+5.1

Substitute the values of U(3) and U(3+h) in the function U(3)=limh0U(3+h)U(3)h as,

U(3)=limh0[5

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