The derivative of the given function by using definition of 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 2.7, Problem 32E

a.

To determine

To calculate:The derivative of the given function by using definition of derivative.

Expert Solution

Derivative of the function is 2+12t .

Explanation of Solution

Given: f(t)=t2t

Concept used:

Definition of derivative: f'(x)=limh0f(x+h)f(x)h

f(t)=t2t be a given function.

It has to find derivative of the function.

f(t)=t2t

f'(t)=limh0f(t+h)f(t)h

f'(t)=limh0(t+h)2t+ht2+th=limh0t2+h2+2htt+ht2+th=limh0h2+2hh+limh0(t+h)th(t+h+t)=2+12t

Hence, derivative of the function is 2+12t .

b.

To determine

Expert Solution

Explanation of Solution

Given: f(t)=t2t

Concept used:

Definition of derivative: f'(x)=df(x)dx

f(t)=t2t be a given function.

It has to find derivative of the function.

f(t)=t2t

f'(t)=df(t)dx

f'(t)=d(t2t)dt=2t12t

Now the graph of function and graph of the derivative is

Respectively.

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