# Differentiation - equation of curves/tangents

Stuck on a few questions... Need help.

2. Find the equation of the tangent at the point (1,-1) to the curve y = 2-(4x^2)+(x^3). What are the co-ordinates of the point where the tangent meets the curve again? Find the equation of the tangent at this point.

3. The point (h,k) lies on the curve y=(2x^2)+18. Find the gradient at this point and the equation of the tangent there. Hence find the equations of the two tangents to the curve which pass through the origin.

4. For the cruve y = (x^3) show that y = 2ax-(a^2)+3 is the equation of the tangent at this point whose x-coordinate is a.
Hence find the coordinates of the two points on the curve, the tangents at which pass through the point (2,6).

Thanks!
for 2)

dy/dx = -8x+3x^2, so plug in 1,-1, to find gradient of tangent.

find equation of the line of the tangent, using change iny/change in x = gradient
(gradient known, and the point 1,-1 value used) i.e. y+1/x-1 = gradient

then use this equation and solve it simultaneously with the equation of the curve to find the coordinates of where they intersect.

put the values of these coordinates into the dy/dx equation and find equation of this line.
arsenalfan.
Stuck on a few questions... Need help.

2. Find the equation of the tangent at the point (1,-1) to the curve y = 2-(4x^2)+(x^3). What are the co-ordinates of the point where the tangent meets the curve again? Find the equation of the tangent at this point.

I think the last part of the question ought to have been ' find the equation of the normal at this point.'

As written the equation of the tangent at BOTH points will be the same - so the question does not really make sense.
arsenalfan.
3. The point (h,k) lies on the curve y=(2x^2)+18. Find the gradient at this point and the equation of the tangent there. Hence find the equations of the two tangents to the curve which pass through the origin.

Here is solution for Q3. I'm leaving you to do the last one.
Hey thanks guys for all your help!!!

For q.2, i checked the question sheet (teacher photo-copied), and i typed out the question correctly... maybe a mistake in her part.... btw the parts I bolded in the questions is the parts i needed help in, not the whole question, but thanks!!

Which program did u use to post those pics steve?
arsenalfan.
Hey thanks guys for all your help!!!

For q.2, i checked the question sheet (teacher photo-copied), and i typed out the question correctly... maybe a mistake in her part.... btw the parts I bolded in the questions is the parts i needed help in, not the whole question, but thanks!!

Which program did u use to post those pics steve?

MathsType for the maths.http://www.dessci.com/en/products/mathtype/

Graphing Calculator, http://www.pacifict.com/

and an Apple Mac.
okay thanks!