Question

Find the difference quotient and simpllify your answer. f(x)= x^2-2x+7, f(4+h)-f(4)/h, h =0

Answer 1

The difference quotient for the function f(x) = x^2 - 2x + 7 is simplified as h + 6. As h approaches 0, the expression simplifies to 6.

Step-by-step explanation:

To find the difference quotient and simplify the answer for the function f(x) = x^2 - 2x + 7, we will calculate f(4+h) - f(4) and then divide by h. However, since it's given that h = 0, we should approach this as a limit problem, taking the limit of the difference quotient as h approaches 0, rather than substituting h with 0 directly which would lead to undefined division by zero.

First, calculate f(4+h):

• f(4+h) = (4+h)^2 - 2(4+h) + 7
• f(4+h) = 16 + 8h + h^2 - 8 - 2h + 7
• f(4+h) = h^2 + 6h + 15

Now, calculate f(4):

• f(4) = 4^2 - 2(4) + 7
• f(4) = 16 - 8 + 7
• f(4) = 15

Then, the difference quotient is:

• (f(4+h) - f(4)) / h
• ((h^2 + 6h + 15) - 15) / h
• (h^2 + 6h) / h
• h + 6

As h approaches 0, the expression simplifies to 6.