vital panther
Hello, can't seem to get the correct answer.
My algorithm goes like:
I differentiate sin (x) - √3 cos (x) and I get cos (x) + √3 sin (x) = 0
I create equation √3 sin (x)/cos (x) = -1
With that, I find that tan (x) = -1/√3 and it is 5π/6
Now I do differentiation a second time to find maxima and after that something goes wrong.
I get:
√3 cos 5π/6 - sin 5π/6 = -√3 *√3/2 - 1/2, which equals -4/2 and gives me an answer of -2.
But actual answer should be just 2. What did I do wrong?
I get the correct answer if I input 5π/6 into sin (x) - √3 cos (x) itself, but then I'm not sure how algorithm should work
violet slate
You are supposed to input that way
You got x when f(x) is maximum. Then find that f(x)
vital panther
But why? When I searched for a solution of a similar problem, they inputted in a second derivative.
violet slate
Second derivative was to determine if the point was a minima or maxima.
f''(x)>0 is minima
f''(x)<0 is maxima
vital panther
So they got that it is a maxima, and, if they had to find value, they would need to actually solve for f(x) = sin π/6 + √3 cos π/6 or am I misunderstanding?
violet slate
Yeah right. And 5pi/6 right?
vital panther
So for my case it's sin 5π/6 - √3 cos 5π/6 which gives us 1/2 + 3/2 = 4/2 = 2 and it's an algorithm which gives me a correct answer, right?
Do you mind me sending full solution so I'm sure I haven't missed anything important?
violet slate
No that's all there is
vital panther
Sorry for bothering, it's the last time - this exam is just really important for me. Looks good?
tranquil hearthBOT
Mark as read
vital panther
Thank you so much! I really appreciate your help
violet slate
Sorry for bothering, it's the last time - this exam is just really important for...
Yeah looks good
Yw
dusty bone
Hi guys, I did a different method using harmonic identities to answer this question
Can someone explain why this method gives the same answer without differentiating ? I found it interesting
I put f(theta) in the form Rsin(theta-a)
violet slate
Hi guys, I did a different method using harmonic identities to answer this quest...
Why R = sqrt. . .. .
dusty bone
Why R = sqrt. . .. .
that’s just how we were taught 💀
idk the theory that well
but u get the coefficients of sin and cos to get r
violet slate
Hmmmm doesn't seem very right
vital panther
+close