calculus help
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Question

calculus help
http://prntscr.com/cy19oh

3mar · Answer

May I help?

amy0799 · Answer

yes please

3mar · Answer

Thanks

3mar · Answer

What did you get?

amy0799 · Answer

I haven't gotten an answer yet. I've plug in 1 into f(x) and got 2. I also took the derivative. But i'm not sure where to go from there

3mar · Answer

It is not like that!
You should to derive the function f(x) firstly

3mar · Answer

Than substitute with y'=o in the derivative to get the x-intercept of the tangent line

amy0799 · Answer

is y=2-pi(x-1) correct?

3mar · Answer

y or y'?

amy0799 · Answer

ignore that equation.
y'(0)=0
I'm not sure what you mean

3mar · Answer

Can you derive y. Just derive!

amy0799 · Answer

I'm not sure what you mean by derive y...

3mar · Answer

derive = get the first derivative of f(x) 
i.e get f'(x)

got it?

3mar · Answer

I will do it for you!

amy0799 · Answer

f'=-sin(pix^2/2)pix

3mar · Answer

$$f(x)=\cos(\frac{ \pi x^2 }{ 2 })+2$$
$$f'(x)=-\sin(\frac{ \pi x^2 }{ 2 })*[\frac{ \pi *2x }{ 2 }]=(-\pi x)\sin(\frac{ \pi x^2 }{ 2 })$$

3mar · Answer

Yes you are brilliant!

3mar · Answer

The question is: where is this function ( f'(x) ) intersect at x-axis
i.e equate it with zero

amy0799 · Answer

so set the derivative equal to 0?

3mar · Answer

Yes, in order to get the x-value at which line strike the x-axis

amy0799 · Answer

x=1.414?

3mar · Answer

Let me check please

3mar · Answer

Do you mind to look at f'(x) graphically?

amy0799 · Answer

I just graphed it

3mar · Answer

Like that? https://www.desmos.com/calculator/pbscbhi40x

amy0799 · Answer

yup, same exact graph as mine

3mar · Answer

Your answer is correct!
x=1.414
and it is not single value by the way

amy0799 · Answer

there's more than one answer?

3mar · Answer

yes, and the evidence is that the curve of f'(x) cross the x-axis many times right and left!

amy0799 · Answer

but isn't 1.414 the only point that is in the boundary from the graph given to us in the question? The question only says x-intercept, not x-intercepts

3mar · Answer

Yes you are right but I just attract your attention for that.

amy0799 · Answer

oh ok.  Thank you so much for the help!

3mar · Answer

I like the students like you, always awake

amy0799 · Answer

haha thank you

3mar · Answer

I thank you that you gave me that chance to help you!