Question

Find f(x + h) − f(x)/h for f(x) = 2x² − 3x - 4.

a) 2x - 3 + h
b) 2x + h - 3
c) 2x + h - 5
d) 2x - 3 - h

Answer 1

To find f(x + h) − f(x)/h for f(x) = 2x² − 3x - 4, we substitute the expressions x + h and x into the function, and then simplify the expression. The simplified expression is 4x + 2h - 3.

Step-by-step explanation:

To find f(x + h) − f(x)/h for f(x) = 2x² − 3x - 4, we substitute the expressions x + h and x into the function, and then simplify the expression.

First, we substitute x + h into the function:
f(x + h) = 2(x + h)² − 3(x + h) - 4
Simplifying this expression:
f(x + h) = 2(x² + 2xh + h²) − 3(x + h) - 4
f(x + h) = 2x² + 4xh + 2h² − 3x - 3h - 4

Next, we substitute x into the function:
f(x) = 2x² − 3x - 4

Now, we subtract f(x) from f(x + h) and divide by h to find the expression:
(f(x + h) − f(x))/h = (2x² + 4xh + 2h² − 3x - 3h - 4 - (2x² − 3x - 4))/h
(f(x + h) − f(x))/h = (4xh + 2h² - 3h)/h
(f(x + h) − f(x))/h = 4x + 2h - 3

Therefore, the correct option is a) 2x - 3 + h