Final answer:
The difference quotient for f(x) = x² - 2 is calculated by finding f(x + h) and subtracting f(x), then dividing by h. The simplified result is 2x + h.
Step-by-step explanation:
The question asks for the calculation of the difference quotient of the function f(x) = x² - 2. This is a common concept in calculus related to the calculation of derivatives. To find the difference quotient, we'll follow the formula given: (f(x + h) - f(x)) / h.
Steps to Calculate the Difference Quotient
First, we'll calculate f(x + h). Here, f(x + h) = (x + h)² - 2.
Expanding the squared term gives us f(x + h) = x² + 2xh + h² - 2.
To find f(x + h) - f(x), we subtract the original function from the expanded function: (x² + 2xh + h² - 2) - (x² - 2).
After simplification, the terms x² and -2 cancel out, leaving us with 2xh + h².
The next step is to divide this expression by h to compute the difference quotient, giving us (2xh + h²) / h.
Finally, when we divide each term by h, we're left with 2x + h.
Thus, the simplified form of the difference quotient for the given function is 2x + h.