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anonymous
 one year ago
Consider the equation below.
f(x) = 3 cos^2x − 6 sin x, 0 ≤ x ≤ 2π
(a) Find the interval on which f is increasing. (Enter your answer in interval notation.)
b)Find the interval on which f is decreasing. (Enter your answer in interval notation.)
c)(b) Find the local minimum and maximum values of f.
d)(c) Find the inflection points.
e)Find the interval on which f is concave up. (Enter your answer in interval notation.)
f)Find the interval on which f is concave down. (Enter your answer in interval notation.)
Please help me work this out!
anonymous
 one year ago
Consider the equation below. f(x) = 3 cos^2x − 6 sin x, 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) b)Find the interval on which f is decreasing. (Enter your answer in interval notation.) c)(b) Find the local minimum and maximum values of f. d)(c) Find the inflection points. e)Find the interval on which f is concave up. (Enter your answer in interval notation.) f)Find the interval on which f is concave down. (Enter your answer in interval notation.) Please help me work this out!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=3\cos^2(x)6\sin(x)\] right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you take the derivative as a first step?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and if so, what did you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.06cos(x)sin(x)6cos(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that looks good i guess the next step is to factor

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0once you factor out the \(6\cos(x)\) it is going to be real easy to see where the derivative is positive and negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah and forturnately for you, since \(\sin(x)\geq 1\) always, you know \(\sin(x)+1\geq 0\) so you can ignore that part when you check tor the sign of the derivative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in other words, the sign of the derivative is completely dependent on the sign of \(6\cos(x)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, im confused as to what my answer would be

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is clear that in order to find the interval over which the function is increasing (decreasing) your only job is to find the interval over which the derivative is positive (negative) yes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok and your derivative isi \[6\cos(x)\left(\sin(x)+1\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the question is, over what interval is the derivative positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i would have to graph it to see it clearly right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you have two factors \[6\cos(x)\] and \[\sin(x)+1\] no you do not have to graph it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it clear that \[\sin(x)+1\geq 0\] for any value of \(x\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that means when you are trying to find if the derivative is positive or negative, you can ignore that factor entirely (because it is never negative) and concentrate only on \(6\cos(x)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know over what intervals between \(0\) and \(2\pi\) that cosine is positive?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then i guess i have to tell you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is positive on \((0,\frac{\pi}{2})\) that is on the right sides of the unit circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0negative on \((\frac{\pi}{2},\frac{3\pi}{2})\) that is the left side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and positive again on \((\frac{3\pi}{2},2\pi)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since your cosine has a \(6\) in front of it, it will be negative where cosine is positive, and vice versa

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so for a) it would be pi/2,3pi/2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0increasing on that interval, yes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and of course decreasing on the remaining intervals

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to find the max and min i would plug in to the equation pi/2 and then 3pi/2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in to the original function of course, not the derivative
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