Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 4 + 3x - x^2, (f(3+h) - f(3))/h

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x), is defined as f(x) = 4 + 3x - x^2.

To determine the difference quotient `(f(3+h) - f(3))/h` , determine the expression for f(3 + h), f(3), subtract the latter from the former and divide the final result by h.

`(f(3+h) - f(3))/h`

= `(4 + 3*(3+h) - (3+h)^2 - (4 + 3*3 - 3^2))/h`

= `(4 + 9 + 3h - 9 - h^2 - 6h - 4 - 9 + 9)/h`

= `(3h - 9 - h^2 - 6h + 9)/h`

= `(-h^2 - 3h)/h`

= -h - 3

= -3

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