Use the difference quotient to determine the slope function for F (x) = 6/3x-2

Answer 1

f(x+h) = 6/(3(x+h)-2) = 6/( 3x+3h-2)

the numerator of the difference quotient is:

f(x+h)- f(x) = 6/(3x+3h-2) - 6/(3x-2) =

6(3x-2) - 6(3x+3h-2)

----------------------------=

(3x-2)(3x+3h-2)

18x - 12 - 18x - 18h + 12

----------------------------

(3x-2)(3x+3h-2)

-18h/ [ (3x-2)(3x+3h-2)]

Dividing by h cancels the h in the numerator...

Limit as h-->0 gives a derivative of:

-18( 3x-2)^(-2)

check by differentiation rules:

Dx [ 6/(3x-2)] =

Dx [ 6 (3x-2)^(-1) ] =

-6(3x-2)^(-2) (3) <-- power rule/chain rule

-18(3x-2)^(-2) <-- yes it checks