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# Differentiation, turning points q Watch

1. 11i) Differentiate and what does this tell you about the number of turning points on the curve?

I've found dy/dx to be and the answer is that there are no turning points, I don't understand how the dy/dx shows that

any help would be great, thanks!
2. what value does dy/dx have at a turning point?

can you make 3x^2+3= that value??
3. (Original post by Magenta96)
11i) Differentiate and what does this tell you about the number of turning points on the curve?

I've found dy/dx to be and the answer is that there are no turning points, I don't understand how the dy/dx shows that

any help would be great, thanks!
dy/dx means the rate of change of y with respect to x, i.e. how much y changes if you change x.
So it's the gradient/slope of the curve.

So if dy/dx = 4, then for every increase in x of 1, y will increase by 4. Basically a ratio of y:x, although someone will strike me down for saying it!

When a curve is at its minima/maxima, it's flat, i.e. the slope is 0, and so dy/dx = 0

Since you showed that 3x^2 + 3 = dy/dx, then for there to be a turning point, 3x^2 + 3 = 0

Try solving that equation and you'll realise that you need to do root(-1), which provides no solutions, ergo there is no minima/maxima.
4. (Original post by The Polymath)
dy/dx means the rate of change of y with respect to x, i.e. how much y changes if you change x.
So it's the gradient/slope of the curve.

So if dy/dx = 4, then for every increase in x of 1, y will increase by 4. Basically a ratio of y:x, although someone will strike me down for saying it!

When a curve is at its minima/maxima, it's flat, i.e. the slope is 0, and so dy/dx = 0

Since you showed that 3x^2 + 3 = dy/dx, then for there to be a turning point, 3x^2 + 3 = 0

Try solving that equation and you'll realise that you need to do root(-1), which provides no solutions, ergo there is no minima/maxima.
Oh okay thanks!

Updated: February 12, 2013
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