Question

Find and simplify the difference quotient of the function f (x) = (3x+1)/(4x) . Find the first derivative f′(x) from the definition, using the rules for limits.

Answer 1

f(x)= 3x/4x +1/4x = 3/4 + 1/4x
f'(x)= lim [f(x+h)-f(x)]/h as h->0
f'(x)= lim (3/4 + 1/4(x+h) -3/4 - 1/4x) /h
f'(x)= lim [(x-h-x)/(4x(h+x))]/h
f'(x)= lim [-h/(4xh(x+h)]= lim (-1/(4x(x+h))] as h->0
f'(x)= -1/(4x^2) <-- answer

Answer 2

is that the derivative of the function or the difference quotient?

Answer 3

the first equation is difference quotient
the last equation is the derivative

Answer 4

aahh got it. i couldn't see the little dash. tanks again

Answer 5

not a problem

Answer 6

what happens to h at the end of the equation?

Answer 7

h goes to zero