   Chapter 3.9, Problem 38E

Chapter
Section
Textbook Problem

# 23-42 Find f. f ′ ′ ( t ) = 4 − 6 / t 4 ,    f ( 1 ) = 6 ,    f ′ ( 2 ) = 9 ,   t > 0

To determine

To find:

The function f(t)

Explanation

1) Concept:

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is Fx+c where c is an arbitrary constant.

Definition:

A function F  is called an antiderivative of f on an interval I if F'x=fx  f for all x in I.

2) Given:

f''t=4-6t4, f1=6, f'2=9, t>0

3) Calculations:

Here f''t=4-6t4

f''t=4-6t-4

The general antiderivative of f'x using rules of antiderivative is,

f't=4t-6×t-3-3+C , Where C is the arbitrary constant

f't=4t+2t-3+C

It is given that f'2=9, therefore, substitute t=2 and f'2=9 to find the value of C

f'2=42+2(2)-3+C

9=8+14+C

34=C

C

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