NationStates Jolt Archive

Yes I know, leaving it to the last moment wasn't very clever but seeming as I've finally persuaded myself to go do it, I'm annoyed that I've got stuck. Oh well at least I did get to Q6 (out of 8).



A curve has the equation y=2x^3-3x^2-12x+15

i) Find dy/dx. Well that I can cope with and got: 6x^2-6x-12

ii) Show that y is increasing when x^2 -x -2>0 :confused: My notes don't help, I'm confused

iii)Hence find the values of x for which y is increasing. I'm guessing I need to complete ii before I can do this.

iv) Find an equation for the tangent to the curve at the point (1,2)

I could do this..I think I just typed in everything before I made notes.. oh well i don't mind if you want to do this 1 too.

ok.

for ii), set the derivative =0 and solve for x. This will give you the points where the function changes direction, so max/min and points of inflection. Next, take the second derivative of the function and sub in the x values you just found. If they're greater than 0 you have a min point, if they're less, you have a max... I don't want to be doing your homework for you, but if your notes aren't helpful I hope that I have been...

Though this is a poor format for math work.

i)6x^2-6x-12

ii) Show that y is increasing when x^2 -x -2>0 :confused: My notes don't help, I'm confused



y is increasing, if dy/dx > 0. OK?
--> dy/dx = 6x^2-6x-12 > 0 | :6
<=> x^2-x-2 > 0

--> y is increasing, if x^2-x-2 > 0.

Yes I know, leaving it to the last moment wasn't very clever but seeming as I've finally persuaded myself to go do it, I'm annoyed that I've got stuck. Oh well at least I did get to Q6 (out of 8).



A curve has the equation y=2x^3-3x^2-12x+15

i) Find dy/dx. Well that I can cope with and got: 6x^2-6x-12

ii) Show that y is increasing when x^2 -x -2>0 :confused: My notes don't help, I'm confused

iii)Hence find the values of x for which y is increasing. I'm guessing I need to complete ii before I can do this.

iv) Find an equation for the tangent to the curve at the point (1,2)

I could do this..I think I just typed in everything before I made notes.. oh well i don't mind if you want to do this 1 too.

i) correct
ii) multiply that inequality by 6, and you have dy/dx>0, this means that y is increasing.
iii) this means finding the values of x for which dy/dx>0. A little analyses of x^2 -x -2 shows that the roots are -1 and 2. It is >0 on the outside of this interval, so it is increasing in ]-infinity, -1[ and ]2,infinity[
iv) (y'-2) = dy/dx(x=1)*(x-1) => y' = -12*x + 14