Let f(x)=1/(3x+1) a. Find f'(4) using limit b.Find f'(4) using formulas

Answer 1

Hi Robert,

I hope this video helps!

Ross

Answer 2

f(x+h) = 1/( 3x+3h+1)

the numerator of the difference quotient is:

f(x+h) - f(x) = 1/(3x+3h+1) - 1/(3x+1)

= [(3x+1) - (3x+3h+1)]/ [(3x+1)(3x+3h+1)]

= [ 3x +1 - 3x - 3h - 1] / [(3x+1)(3x+3h+1)]

= (-3h)/[(3x+1)(3x+3h+1)]

DIviding by h:

-3/[(3x+1)(3x+3h+1)]

limit as h-->0 -3/(3x+1)^2

Power Rule/Chain Rule:

The function is (3x+1)^(-1)

the derivative is (-1)(3x+1)^(-2) * 3

= -3/(3x+1)^2

f'(4) = -3/169