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Sketching a curve after differentiation

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1. Using differentiation, find the turning points of the function y = x3 – 2x2 + 1 and sketch its curve.
2. (Original post by Deannnn97)
Using differentiation, find the turning points of the function y = x3 – 2x2 + 1 and sketch its curve.
What about it? Will I get paid if I do your homework for you? Show some attempt!
3. (Original post by Deannnn97)
Using differentiation, find the turning points of the function y = x3 – 2x2 + 1 and sketch its curve.
dy/dx = 3x2 - 4x
= x(3x - 4)
Turning points are (0,0) (1.33,0)
4. (Original post by Trapz99)
dy/dx = 3x2 - 4x
= x(3x - 4)
Turning points are (0,0) (1.33,0)
Thanks, so would this be a u shape or a n shape? I am not sure whether the shape comes from the +/-x or the +/- of the number?
5. (Original post by Trapz99)
dy/dx = 3x2 - 4x

= x(3x - 4)
Turning points are (0,0) (1.33,0)
You missed a step, you need to sub the x values back into y to find the y coordinates at the stationary point.

(Original post by Deannnn97)
Thanks, so would this be a u shape or a n shape? I am not sure whether the shape comes from the +/-x or the +/- of the number?
Neither, it's a cubic curve.
6. Sorry I misread the question.

When you draw the graph for x3 - 2x2 + 1 that's a cubic curve and not u or n shaped
7. (Original post by Trapz99)
No I didn't miss anything.

It's not a cubic curve. 3x2 - 4x doesn't have any cube
That's

The curve is written in the OP.
8. (Original post by Trapz99)

When you draw the graph for x3 - 2x2 + 1 that's a cubic curve and not u or n shaped
you need to sub your X values into the original equation for the stationary points, not the differential
a) dy/dx = 3x2 - 4x
0 = x (3x - 4)
x = 1.33 x =0
y = -5/27 y = 1
So (1.33, -0.1852) and (0,1) are turning points
10. (Original post by Bananapeeler)
you need to sub your X values into the original equation for the stationary points, not the differential
Lol yeah I messed up
11. Do you understand why we have to use differentiation to be able to sketch the curve more accurately, or are you doing it for the sake of it?
12. (Original post by RDKGames)
What about it? Will I get paid if I do your homework for you? Show some attempt!
Homework at this time of year?
13. (Original post by ODES_PDES)
Homework at this time of year?
Perhaps the summer schools are stepping it up a notch.

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