Question

Find f(x h)−f(x) given the following function: f(x) = −7x − 3x².

a) -3h - 3h²
b) -7 - 3h
c) 3h + 3h²
d) 7 + 3h

Answer 1

To find f(x + h) - f(x), substitute (x + h) into the function f(x) and subtract f(x) from it. The answer is -7h - 6xh - 3h².

Step-by-step explanation:

To find f(x + h) - f(x), we need to substitute (x + h) into the function f(x) and then subtract f(x) from it.

Given f(x) = -7x - 3x², we can substitute (x + h) into the function:

f(x + h) = -7(x + h) - 3(x + h)²

Expanding and simplifying:

f(x + h) = -7x - 7h - 3(x² + 2xh + h²)

f(x + h) = -7x - 7h - 3x² - 6xh - 3h²

Now, subtract f(x):

f(x + h) - f(x) = (-7x - 7h - 3x² - 6xh - 3h²) - (-7x - 3x²)

f(x + h) - f(x) = -7x - 7h - 3x² - 6xh - 3h² + 7x + 3x²

f(x + h) - f(x) = -7h - 6xh - 3h²

Hence, the answer is -7h - 6xh - 3h² (option a).