anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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
anonymous
  • anonymous
is that the derivative of the function or the difference quotient?
anonymous
  • anonymous
the first equation is difference quotient the last equation is the derivative

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anonymous
  • anonymous
aahh got it. i couldn't see the little dash. tanks again
anonymous
  • anonymous
not a problem
anonymous
  • anonymous
what happens to h at the end of the equation?
anonymous
  • anonymous
h goes to zero

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