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12. Find and Simplify the Difference Quotient for F(x)=2x^2+3x-6 A. 4x+2h+3 B. 2x+2h+3 C. 4xh+2h^2+3h D. 2h+3

Question

12. Find and simplify the difference quotient for f(x)=2x^2+3x-6
a. 4x+2h+3
b. 2x+2h+3
c. 4xh+2h^2+3h
d. 2h+3

12. Find and simplify the difference quotient for f(x)=2x^2+3x-6 a. 4x+2h+3 b. 2x+2h+3 c. 4xh+2h^2+3h d. 2h+3

Solution

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Felipe Elite · Tutor por 8 anos

Resposta

To find and simplify the difference quotient for \( f(x) = 2x^2 + 3x - 6 \), we need to compute the expression: First, let's find \( f(x+h) \): Expanding \( (x+h)^2 \): So, Next, we subtract \( f(x) \) from \( f(x+h) \): Simplify by canceling out the common terms: Now, divide by : Simplify by factoring out in the numerator: Cancel : Thus, the simplified difference quotient is: The correct answer is: