   Chapter 10.6, Problem 30E 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. S ( t ) = 1.4 t 2 ; S ′ ( − 1 )

To determine

To calculate: The value of the derivative S(1) for the function S(t)=1.4t2.

Explanation

Given Information:

The provided function is S(t)=1.4t2.

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,

(ab)2=a2+b22ab

Calculation:

Consider the function, S(t)=1.4t2

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,

S(a)=limh0S(a+h)S(a)h

Substitute a=1 into the above formula,

S(1)=limh0S(1+h)S(1)h

Here S(1)=1.4(1)2, then

S(1+h)=1.4(1+h)2

Substitute the values of S(1) and S(1+h) in the function S(1)=limh0S(1+h)S(1)h as,

S(1)=limh0[1

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