# Tofind: the function using its first derivative.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 53RE
To determine

## Tofind:the function using its first derivative.

Expert Solution

Thefunction using its first derivative f(t)=t2+3Cost+2 .

### Explanation of Solution

Given:

f(t)=2t-3sint,f(0)=5 .

Concept used:

Antiderivative=integration

f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

xndx=xn+1n+1 .

Calculation:

f(t)=2t-3sint,f(0)=5 .

f(t)dt=2tdt-3sintdt .

f(t)dt=t2+3Cost+C

f(t)=t2+3Cost+C .

f(0)=(0)2+3Cos0+C

5=(0)2+3Cos0+C

C=2 .

f(t)=t2+3Cost+2 .

Hence the function using its first derivative f(t)=t2+3Cost+2 .

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