   Chapter 2.2, Problem 21E

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Textbook Problem
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# Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. f ( t ) = 2.5 t 2 + 6 t

To determine

To find: the derivative of the function by using the definition of derivative. And to state the domain of function and domain of derivatives of the function.

Explanation

Definition of derivative is

f'x= limh0 fx+h-f(x)h

Here ft=2.5t2+6t

Therefore, ft+h=2.5t+h2+6t+h=2.5t2+2th+h2+6t+6h(by simplifying the square term and distributing the 6 and and 2.5 we have,

ft+h=2.5t2+5th+2.5h2+6t+6h

Substitute these values in the formula to get,

f't= limh0 2.5t2+5th+2.5h2+6t+6h -2.5t2+6th

=limh0 2.5t2+5th+2

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