Author Topic: query (Read 541 times) Tweet Share

95atar · « **on:** May 25, 2013, 09:20:15 pm »

find the coordinates of the points on the curve y=4x^2+5 at which the tangents drawn to the curve pass through the point (0,4)

BubbleWrapMan · « **Reply #1 on:** May 25, 2013, 09:29:28 pm »

Generally, if we have a tangent at $(p,f(p))$ , the equation of the tangent is given by

$y=f'(p)(x-p)+f(p) \iff y=f'(p)x+f(p)-pf'(p)$

so the $y$ -intercept of the tangent is $f(p)-pf'(p)$ . If we want this to equal 4, we solve $f(p)-pf'(p)=4\iff 4p^2+5-p(8p)=4\iff 4p^2=1\iff p=\pm\frac{1}{2}$ .

So the required points are $\left(-\frac{1}{2},6\right)$ and $\left(\frac{1}{2},6\right)$ .

Search the forums now!

We have moved!

Author Topic: query (Read 541 times) Tweet Share

95atar

query

BubbleWrapMan

Re: query

Recent Posts

User:
Password: