Find x co-ordinates of the turning points of a function

druuuuuuuunnk
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Hi!

Find the x co-ordinates of the turning points of a function

Y=2x^3+36x-1

Determine the nature of the turning points.

I've been reading up on differentiation, I understand but I'm unsure what to do here. If someone could give me some helpful steps so I could learn to do this for my exam tomorrow I'd be grateful

Thanks
 
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druuuuuuuunnk said:
I've been reading up on differentiation, I understand but I'm unsure what to do here. If someone could give me some helpful steps so I could learn to do this for my exam tomorrow I'd be grateful

You tell me. What is the slope of a turning point of the graph?
 
gb7nash said:
You tell me. What is the slope of a turning point of the graph?

Its the gradient? Its the solution of to find x that I'm confused about. Do I differentiate it to simply it? Is that the answer the questions for or what else should I be looking at to solve it.
 
Start by answering gb7nash's question, then we can go from there.
 
druuuuuuuunnk said:
Its the gradient? Its the solution of to find x that I'm confused about. Do I differentiate it to simply it? Is that the answer the questions for or what else should I be looking at to solve it.

Seems like you're asking us to help you not read or listen in class (sorry). Ask (and look up) the following:

- what characterized a turning point?
- what determines whether it is min, max or saddle point?

Really, if someone does any more for you, they're just doing your work.
 
Ok thanks, I look those things up. I appreciate the help.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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