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
Solution
4.5
(250 Votos)
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: