Question

Consider the function f(x)=5x²−2x−6. Simplify the difference quotient expression by evaluating f(x+h) and subtracting f(x).

Answer 1

To find the difference quotient for the function f(x)=5x²-2x-6, evaluate f(x+h), expand, and subtract f(x). This process will simplify the difference quotient expression.

Step-by-step explanation:

The student is asking to simplify the difference quotient for the function f(x)=5x²-2x-6. To do this, we must evaluate f(x+h) and subtract f(x) from it. The difference quotient can be expressed as (f(x+h)-f(x))/h.

First, we evaluate f(x+h) which is f(x+h) = 5(x+h)²-2(x+h)-6. We need to expand this and simplify before subtracting f(x).

Expanding f(x+h) gives us 5(x²+2xh+h²)-2x-2h-6. Substituting f(x) into the expression, we will have 5x²-2x-6 which we then subtract from f(x+h) to obtain our simplified difference quotient expression.