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NathanJHW
 one year ago
In this problem, you will investigate the family of functions h(x) = x + cos(ax) , where a is a positive constant such that 0 < a < 4.
NathanJHW
 one year ago
In this problem, you will investigate the family of functions h(x) = x + cos(ax) , where a is a positive constant such that 0 < a < 4.

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NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1A. Graph the curves y(x) = x + cos(¼x) and y(x) = x + cos(4x)

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1B. For what values of a will h(x) have a relative maximum at x = 1?

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1C. Which values of a make h(x) strictly decreasing? Justify your answer.

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1I need help with A and C. Already got B.

phi
 one year ago
Best ResponseYou've already chosen the best response.1How far did you get ? Can you use Geogebra or other plotting tool?

phi
 one year ago
Best ResponseYou've already chosen the best response.1or do you have to do it by hand ?

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1Didn't even think about using a graphing tool for part A. I'll do that now.

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1Alright I got part A now, can you help me with C?

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1I think we might need to use the work I did for part B so i'll post it.

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1h'(x) = 1 a sin (ax); h'(1) = 0 h'(1)= 1  a sin (a) = 0 1 a sin (a) = 0 1 = a sin a a is approx: + 9.3 , + 6.4, + 2.8 , + 1.1

phi
 one year ago
Best ResponseYou've already chosen the best response.1strictly decreasing means as x increases f(x) gets smaller.

phi
 one year ago
Best ResponseYou've already chosen the best response.1I don't see how to be decreasing when we are adding x

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1That's what I thought too, but how should I justify?

phi
 one year ago
Best ResponseYou've already chosen the best response.1strictly decreasing means that at every x the slope of the function is never 0 or positive. i.e. the slope is always negative. f'(x) = 1  a sin(ax) and because the sin(ax) will be negative for 1/2 of its period, the a sin(ax) adds to 1 and that is clearly not negative.

phi
 one year ago
Best ResponseYou've already chosen the best response.1btw, how did you solve a sin a = 1 for a ? (and you should restrict your a's to the interval: a is a positive constant such that 0 < a < 4. )

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1So then it would only be 1.1 and 2.8?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. But how did you find those values?

phi
 one year ago
Best ResponseYou've already chosen the best response.1oh, because it looks hard to solve (without the wolf)

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1exactly, that's why I used it

NathanJHW
 one year ago
Best ResponseYou've already chosen the best response.1Alright, well thanks for your help!
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