   Chapter 2.2, Problem 22E

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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 ( x ) = 4 + 8 x − 5 x 2

To determine

To find: the derivative of the function by using the definition of derivative. State the domain of function and domain of derivative of its function.

Explanation

Definition of derivative is

f'x= limh0 fx+h-f(x)h

Here fx=4+8x-5x2

Therefore, fx+h=4+8(x+h)-5(x+h)2

By distributing 8 in second term and simplifying the square

fx+h=4+8x+8h-5x2+2xh+h2

By distributing -5 in last term

fx+h=4+8x+8h-5x2-10xh-5h2

By substituting these values in the formula

f'x= limh0 4+8x+8h-5x2-10xh-5h2-(4+8x-5x2)h

=limh0 4+8x+8<

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