## LotusWings 2 years ago 24: find Point of Inflection and discuss concavity of graph of func. 40: find all relative extrema, use 2nd derivative test where applicable. 58: Water is running into the vase shown @ a constant rate. (a) graph depth of water in vase as a function of time. (b) Does the function have any Extrema? Explain. (c) Interpret the PI (Point of Inflection) of the graph of d.

1. LotusWings

My work:

2. LotusWings

3. LotusWings

Or anyone really :P

lol, um, meanwhile, can you type the original eq.?

5. LotusWings

okay

6. LotusWings

#24: f(x) = sinx+cosx [0, 2Pi] #40: f(x) 2sinx + cos2x [0, 2Pi] I think mostly i'm having issues with just finding the derivative of trig functions. Oh, and my friend helped me with number 58 so it's all cool.

for question 40, for the test, you let f'(x) = 0 and solve for x. then, you apply the x-values into f''(x) to test for maxima or minima

point of inflexion in 24 is found by letting f''(x)=0. also, you'll need the double angle formulas.

9. LotusWings

yeah, i know how to = 0 but I don't know how to solve the trig to find the x :(

10. LotusWings

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lol okay, i'll do one as an example. $$-sin x- cos x=0$$ $$cos x+ sin x=0$$ applying the $$Rcos(x-\alpha)$$ form, where $$R=\sqrt{1+1}$$, $$\alpha = tan^{-1} 1=\pi/4$$ $$\sqrt2 cos (x-\pi/4)=0$$ solve for x.

12. LotusWings

i don't think i've ever seen the Rcos(x−α) form before. :O

hmm, another way is letting sin x = cos(pi\2 -x) but this is much more complicated, but yes, this is the way to solve these type of eqs. for angles with the same cosine, i.e. $$\cos \theta= \cos \alpha$$,$$\theta = 2n\pi \pm \alpha$$

14. LotusWings

you're welcome :)

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