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I'm confused on how to find the difference quotient of a number.

I started out by defining my function.

Clear[f]; f[x_] = (12 x)/(Sqrt[(x^2 - 5)])

Then I found the difference quotient 

DifferenceQuotient[f[x], {x, h}]

I figured to find the difference quotient at x=3 I would just do 

DifferenceQuotient[f[3], {x, h}]

but that just outputs 0 and I don't believe that is correct.

awild
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  • try : DifferenceQuotient[f[x], {x, h}] /. x->3 – kglr Sep 24 '17 at 17:40
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    "that just outputs 0 and I don't believe that is correct." - what did you expect the difference quotient of a constant was going to evaluate to? – J. M.'s missing motivation Sep 24 '17 at 17:54
  • Following on the comment of @kglr, DifferenceQuotient will look in the first argument for the variable that you provide in the second argument. Note that f[3] is not an expression in the variable x. – Alan Sep 24 '17 at 18:00
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    Note that Limit[DifferenceQuotient[f[x], {x, h}] /. x -> 3, h -> 0] == f'[3] evaluates to True – Bob Hanlon Sep 24 '17 at 18:23

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