Given f(x)=7/x, find the limit: lim h→0 [f(x+h)−f(x)]/h

Question

I have zero clue how to do this...

Answer 1

f(x+h) = 7/(x+h)

f(x+h) - f(x) = 7/(x+h) - 7/x = [ 7x - 7(x+h)]/ [x(x+h)]

= [ -7h ]/ [ x(x+h) ]

Dividing that by h: -7 / [ x (x+h) ] = -7 / [x(x+h)]

Finally the limit as h tends to zer0, gives the derivative of -7/ x^2

Note that this result agrees with the power rule: Dx [ 7/x] = Dx [ 7x^(-1)] = -7x^(-2) = -7/x^2