use the difference quotient to determine the slope function for F(x)=3x^2 - 4x - 1

Answer 1

f(x+h)=

3(x+h)^2 - 4(x+h)-1 =

3(x^2+2xh+h^2) - 4(x+h) - 1 =

3x^2 + 6xh + 3h^2 - 4x - 4h - 1

subtracting f(x) leaves:

6xh + 3h^2 - 4h

dividing by h:

6x + 3h - 4

finally, lim h->0

6x-4

which agrees with the power rule