Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can anyone check my math on the following equation? I'm trying to find the slope of the tangent at$ x=3.5 $ for $$ y = 0.000005x^4 - 0.0014x^3 + 0.1007x^2 - 4.4776x + 168.79$$

It's been a very long time since I've done calculus, and I THINK what I need to do is find the derivative before plugging$ x=3.5$ in...

$$y' = 0.00002x^3 - 0.0042x^2 + 0.2014x - 4.4776$$ $$y'(3.5) = 0.000000000000343 - 0.00021609 + 0.7049 - 4.4776$$ $$y'(3.5) = -3.772916089999657$$

share|cite|improve this question
No problem with derivative. Problem with substitution. For example first term should be $0.0008575$. – André Nicolas Oct 9 '12 at 16:33
as long as you did not make a numerical mistake, it should be correct... – David Hoffman Oct 9 '12 at 16:41
After corrections, I think it is this... y'(3.5) = -4.142085625 – Szuturon Oct 9 '12 at 18:36
Your previous answer was closer to the truth. I get about $-3.8232925$. No guarantees! – André Nicolas Oct 9 '12 at 18:48
Ok. I don't know why I didn't just do this from the start. I went ahead and plugged in "=0.00002*(3.5^3)-0.0042*(3.5^2)+0.2014*(3.5)-4.4776" into Excel. I have -3.8232925 now. I suck. – Szuturon Oct 9 '12 at 20:01
up vote 4 down vote accepted

Your derivative was calculated correctly. The substitution has mistakes, due to incorrect use of the calculator. For example, you wanted to evaluate $0.00002x^3$ where $x=3.5$. What you did is almost certainly to multiply $0.00002$ by $3.5$, and then take the power. So you calculated $(0.00002x)^3$. This is $(0.00002)^3(3.5)^3$, very tiny.

What you need to do is to calculate $(3.5)^3$ first, and then multiply the result by $0.00002$. There is a similar issue with the evaluation of the next term.

share|cite|improve this answer
See... this is why I doubted myself. Years later and I'm still making stupid mistakes like this... I suppose my calculus prof woulda marked this 1/3 and that would be merciful :P – Szuturon Oct 9 '12 at 18:29
@Szuturon: It was just a minor slip of the fingers, much more likely in this calculator age than it used to be. About the $1/3$, I would probably give full marks, unless the slip results in an answer to an "applied" problem that is physically unreasonable. And I would still give full marks if the person said it is unreasonable. But with a multiple choice or "exact answer" test, so undeservedly popular nowadays, the mark would probably be $0$. Another reason not to have such tests. – André Nicolas Oct 9 '12 at 18:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.