# Just a little question i need help with.

• Nov 12th 2012, 11:59 PM
Walshy4119
Just a little question i need help with.
1. The curve C is given by the equation y=mx3-x2+8x+2, for a constant m
A) find dy/dx

The point P lies on C, and has the x-value 5
The normal to C at P is parallel to the line given by the equation y+4x-3=0.

B)find the gradient of the curve at C at P.

Hence find:
C) (I) the value of m,

(ii) the y-value at p.

For A) i got:
dy/dx=3mx2-x+8

I'm not really sure how to carry on with it now any help would be brilliant :)
Thanks.
• Nov 13th 2012, 12:19 AM
MarkFL
Re: Just a little question i need help with.
b) Evaluate $\displaystyle \frac{dy}{dx}\left|_{x=5}$
c) The statement "The normal to C at P is parallel to the line given by the equation y+4x-3=0" tells us that the derivative of y with respect to x at x = 5 is the negative reciprocal of the slope of the given line. So, find the slope of the line $\displaystyle y+4x-3=0$, invert it, negate it and equate this to $\displaystyle \frac{dy}{dx}\left|_{x=5}$.
i) Solve the resulting equation for $\displaystyle m$.
ii) We are told the xcoordinate of point P is 5, so to find the y-coordinate evaluate $\displaystyle y(5)$.