# Differentiation question ... need help!!!

• Nov 29th 2008, 07:10 AM
jisaac
Differentiation question ... need help!!!
A curve has the equation y=root x(k-x) where k is a constant.
Given that the gradient of the curve is root 2 at the Point P where x=2.

a. find the value of k.

b.show that the normal to the curve at P has the equation
x+root 2y=c where c is an integer to be found.
• Nov 29th 2008, 07:52 AM
jisaac
i got the solutions k = 2.5/2.0625
is the right???
• Nov 29th 2008, 08:11 AM
running-gag
I got $k\;=\;12+4\sqrt{6}$
How did you get your value ?
• Nov 29th 2008, 08:22 AM
jisaac
• Nov 29th 2008, 08:29 AM
running-gag
You made a mistake in the differentiation of y
$(u^n)'\;=\;nu'u^{n-1}$

You forgot u'
• Nov 29th 2008, 08:33 AM
jisaac
what's u'???
i thought the first derivative is defined as:
dy/dx = n(x^(n-1))
• Nov 29th 2008, 08:41 AM
running-gag
The first derivative of y=x^n is y'=n x^(n-1)

But the first derivative of y=(u(x))^n is y'=n u'(x) (u(x))^(n-1)

Here u(x)=kx-x² and n=1/2