Confirmation and help:

A curve has the equation:
y= x^3 +3x^2 -9x + k, where k is a constant

(i) write down an expression for dy/dx

My solution:

dy/dx= 3x^2 + 6x - 9

Is it correct?

(ii) Find the x-coordinates of the two stationary points on the curve.

My solution

x=1 or x=-3

Is it correct?

(iii) Hence find the two values for K for which the curve has a stationary point on the x-axis.

Help please.

Question

Confirmation and help:

A curve has the equation:
y= x^3 +3x^2 -9x + k, where k is a constant

(i) write down an expression for dy/dx

My solution: 

dy/dx= 3x^2 + 6x - 9

Is it correct?

(ii) Find the x-coordinates of the two stationary points on the curve.

My solution

x=1 or x=-3

Is it correct?

(iii) Hence find the two values for K for which the curve has a stationary point on the x-axis.

Help please.

anonymous · Answer

Yeah that's right. For (iii), remember that k disappears when you take the derivative. So the stationary points are the same that you found in (ii). So, now find what y = at those two values of x. Then, set k so that y = zero at those stationary points. I found that when x = 1, k had to be 5, and when x = -3 k has to be -27. I just rushed through, so might not be right... but I think that's the general idea... It does seem to say that you'll need two different values for k.

anonymous · Answer

I'm confused... Can you show it in steps?

anonymous · Answer

Well you've got (i) and (ii) right, you don't need help with that, right?

For the stationary point, I think that is when the derivative equals zero or something? I've forgotten that terminology, but that's what you've said it is, and I think that's right.

So, the stationary points are the two found in (ii). The question asks you to choose a value for k so that the stationary point is on the x axis. That means that y = 0. So, calculate the value of y when x equals the stationary points, which is x = 1 and x = -3. You'll get some number plus k. Set k so that the sum of the two is equal to zero. This means that the stationary point is on the x axis.

Maybe that just sounds more confusing...

anonymous · Answer

Yes... Can you maybe show the steps out...?

anonymous · Answer

If you read what I wrote then it should be clear.

anonymous · Answer

I did, but my brain is more visual... I can't comprehend.... If you write it out in steps, bit by bit, it might help

anonymous · Answer

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The two x's are the stationary points of the function y. You want to calculate what function is equal to at those points, and set k equal to the negative of that value, so that the graph is moved up or down so that the point x occurs on the x axis.