Use the difference quotient to determine the slope function for f (x) = 3x^ - 4x - 1

Answer 1

The difference quotient is defined as:

[f(x+h) - f(x)]/ h

first let's find f(x+h):

f(x+h) = 3(x+h)² - 4(x+h) - 1

f(x+h) = 3(x²+h²+2xh) - 4x - 4h - 1

f(x+h) = 3x²+3h²+6xh - 4x - 4h - 1

next let's find f(x):

f(x) = 3x²- 4x - 1

now we subtract to find f(x+h) - f(x):

[3x²+3h²+6xh - 4x - 4h - 1] - [3x²- 4x - 1]

= 3h² + 6xh - 4h

last, we divide the whole thing by h:

[3h² + 6xh - 4h]/h = 3h + 6x - 4

And that's our answer!

3h + 6x - 4

Hope this helps :)