Question

If f(x) = -2x² + 5x - 10, completely simplify the expression (f(x+h) - f(x))/h A) -2h + 5 B) -2h + 5 - 10/h C) -2h + 10 D) -2h - 5 + 10/h

Answer 1

To simplify the expression (f(x+h) - f(x))/h, substitute the given expression of f(x) into the formula and combine like terms to get the simplified expression -4x - 2h + 5.

Step-by-step explanation:

To simplify the expression (f(x+h) - f(x))/h, we first need to substitute the given expression of f(x) into the formula. So, we have:

(f(x+h) - f(x))/h = (-2(x+h)² + 5(x+h) - 10 - (-2x² + 5x - 10))/h

Simplifying further, we get:

(f(x+h) - f(x))/h = (-2x² - 4hx - 2h² + 5x + 5h - 10 + 2x² - 5x + 10)/h

By combining like terms and simplifying, we get:

(f(x+h) - f(x))/h = (-4hx - 2h² + 5h)/h = -4x - 2h + 5

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