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Evaluate the difference quotient (f(x+h)-f(x))/(h) for the function f(x)=3x-x^(2)

User Kausty
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Final answer:

The difference quotient for the function f(x) = 3x - x^2 is 3 - 2x - h.

Step-by-step explanation:

The difference quotient for the function f(x) = 3x - x^2 can be evaluated using the formula (f(x+h) - f(x))/h.

Substituting the given function into the formula, we have:

((3(x+h) - (x+h)^2) - (3x - x^2))/h

Simplifying this expression, we get:

(3x + 3h - (x^2 + 2xh + h^2) - 3x + x^2)/h

Combining like terms, we can cancel out the 3x and x^2 terms, resulting in:

(3h - 2xh - h^2)/h

Factoring out an h from the numerator:

(h(3 - 2x - h))/h

Cancelling out the h terms, we are left with:

3 - 2x - h

Therefore, the difference quotient for the function f(x) = 3x - x^2 is 3 - 2x - h.

User Jeffasante
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