Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The question is as follows: Find the equation of the tangent to the curve $y = xe^{2x}$ at the point $(\frac{1}{2}, \frac{e}{2})$.

Now I figured out that $\frac{dy}{dx} = e^{2x}(2x+1)$, and that when I plug in $x=1/2$ then I get that the slope = $2e$.

So at this point I have the original curve's equation, the equation of its differential, the fact that the slope of the tangent at the given point is $2e$ and that this tangent also passes through the point $(\frac{1}{2}, \frac{e}{2})$. But I can't seem to arrive at the equation of this tangent.

The answer is

\begin{equation} y = 2ex - \frac{e}{2} \end{equation}

but how they got there, I don't know. I've checked other find the equation of a tangent line to a curve questions, but still haven't figured my way to that answer. It seems there's something wrong with my assumption that the equation of the tangent line is of the form $y=mx+c$. But how do I know which form it should take?

Edit

Sorry - I'd written the target answer above wrong. I edited it to correct it.

share|improve this question
    
Do you mean $2ex-e/2$? –  Michael Albanese Jan 31 '13 at 10:58
    
I think it should be $2ex-\frac{e}{2}$ so that it passes through $(\frac{1}{2},\frac{e}{2})$. –  Strin Jan 31 '13 at 11:13
    
That that you say is the answer can't possibly be correct as it is not the equation of a straight line... –  DonAntonio Jan 31 '13 at 12:49
    
You're right... it was 2ex not e^x, I've edited the question. But even with this I seem to be making some fundamental mistake and can't arrive at it! –  user60395 Jan 31 '13 at 13:43

2 Answers 2

up vote 0 down vote accepted

The equation of a line of slope $m$ passing through a point $(x_0,y_0)$ is

$$y-y_0 = m (x - x_0)$$

Here, $m=2 e$, $x_0 = \frac{1}{2}$, and $y_0 = \frac{e}{2}$. Plug away.

share|improve this answer

so 1. F(x) = xe^2x

  1. F(x)'= e^2x (2x + 1)

  2. slope when you substitute x=1/2 = 2e

  3. y - e/2 = 2e (x - 1/2)

y= 2ex - e + e/2

Y= 2ex - e/2

share|improve this answer

Your Answer

 
discard

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.