Question
find the maximum value of
f(x)= 3cos(x)-2sin(x)
I know you have to take the derivative but after the derivative I don't know how to solve it.
f'(x)=-3sin(x)-2cos(x)=0
I don't know what to do after this please help.
f(x)= 3cos(x)-2sin(x)
I know you have to take the derivative but after the derivative I don't know how to solve it.
f'(x)=-3sin(x)-2cos(x)=0
I don't know what to do after this please help.
Answers
so far ok
-3sin(x)-2cos(x)=0
3sinx = -2cosx
sinx/cosx = -2/3
tanx = -2/3
construct your triangles in quad II and IV
for both the hypotenuse is √13
in quad II
y = 3(-3/√13) - 2(2/√13) = -13/√13
in quad IV
y = 3(3/√13) -2(-2/√13) = 13/√13
so the max value is 13/√13
-3sin(x)-2cos(x)=0
3sinx = -2cosx
sinx/cosx = -2/3
tanx = -2/3
construct your triangles in quad II and IV
for both the hypotenuse is √13
in quad II
y = 3(-3/√13) - 2(2/√13) = -13/√13
in quad IV
y = 3(3/√13) -2(-2/√13) = 13/√13
so the max value is 13/√13
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