How would I get the graph for this and what would it look like?
g(x)=
e^((−3x+2sinx)/6)
------------------
(3+2cosx)

Question

How would I get the graph for this and what would it look like?
g(x)= 
e^((−3x+2sinx)/6) 
------------------ 
     (3+2cosx)

anonymous · Answer

Or do I need to get it from the derivative?

shubhamsrg · Answer

yes,,find g'(x)..check if g'(x) = 0 has some roots..which will give maxima minima.. rest should be easier..

anonymous · Answer

as @shubhamsrg  says, you'll need to do some curve sketching using derivatives but just to verify if your answer is on the right track, you can always verify with wolfram...

anonymous · Answer

I have go there derivative which is a fractions but should just use the numerator only to get the graph without the exponential part?

shubhamsrg · Answer

i'll post the solution,,gimme few mins..

anonymous · Answer

ok

shubhamsrg · Answer

i hope g'(x) =0  gives you sin x= 1/2 ??

anonymous · Answer

Yes and 5/2

shubhamsrg · Answer

sin x cant be equal to 5/2 as 5/2 > 1 ..

anonymous · Answer

ok

shubhamsrg · Answer

can you give me a general solution for x here then ?

anonymous · Answer

-4sinx+12sinx-5

anonymous · Answer

Think he means 5/2 for a turning point.....

shubhamsrg · Answer

whats this ? i meant that general solution is x=2npi + pi/6 and 2npi + 5pi/6

shubhamsrg · Answer

which means your graph will attain maxima and minima for these values of x...

shubhamsrg · Answer

to check this ,,we check when is g'(x)>0 and when <0 ..can you tell me that ?

anonymous · Answer

Usually you test the second derivative

shubhamsrg · Answer

well second derivative can also be used,,it tells the rate of change in slope..but checking with first derivative will also work here as it will tell us when the slope is positive and negative..

anonymous · Answer

the interval is 0(equal and less) and 2pi ( equal to and less then)

shubhamsrg · Answer

well you conclude that for x=2npi +5pi/6 ,,there is a maxima ,,and for x=2npi + pi/6 ,,theres a minima..

shubhamsrg · Answer

well you need not check if g'(x) > 0 or not for this,,you could have dont it simply by substituting x with these values in g(x) to check which 1 is maxima and minima..

shubhamsrg · Answer

altough the result which you should obtain by checking should yield the same thing.. hope am clear till now? then i'll proceed,,

shubhamsrg · Answer

??

anonymous · Answer

This is what computers were made for http://www.wolframalpha.com/input/?i=g%28x%29%3D++e^%28%28%26%238722%3B3x%2B2sinx%29%2F6%29%2F%283%2B2cosx%29&x=0&y=0