For the function f ( x ) = − 2x^2 + 2x + 8 , evaluate and fully simplify each of the following. f ( x + h ) =

f ( x + h ) − f ( x ) =

Step-by-step explanation:

Given the function:

Find

Recall the identity to square a binomial:

Squaring the binomial:

Multiplying:

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To compute f ( x + h ) - f ( x ), we use the last result:

Multiplying:

Simplifying similar terms:

Factoring:

Note: This expression is commonly used to compute the first derivative of a function by its definition.

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation: