First derivative of f(x)=3sin^2(x)

Question

anonymous · Answer

$$f(x)=3\sin ^{2}(x)$$

bahrom7893 · Answer

$$f(x) = 3(Sin(x))^2$$$$f'(x) = 2*3*Sin(x)*(Sin(x))'$$

anonymous · Answer

6sin(x)cos(x). right?

bahrom7893 · Answer

Yup

anonymous · Answer

this is my original problem and that derivative isnt in the answer options!

bahrom7893 · Answer

It's asking for a derivative test, not the derivative.

bahrom7893 · Answer

This is tedious... ugh.. ok.. here goes..

bahrom7893 · Answer

f'(x) = 0 when x = 0
$$f''(x) = -6Sin^2(x)+6Cos^2(x)=-6(Sin^2(x)-Cos^2(x))$$

bahrom7893 · Answer

Now you know that f'(x) = 0 when x = 0. You need to check the signs of f'' before and after x = 0

bahrom7893 · Answer

pick any negative number and evaluate that expression, then record the sign before 0. Pick any positive number and evaluate it again and record the sign after 0.

anonymous · Answer

Ok. I understand what your saying but what i dont understand Is why the first derivative isnt in the answers as "f'(x) ="

anonymous · Answer

Thats what im stuck on :/

bahrom7893 · Answer

f'(x) = 0 and is near 0 are used pretty interchangeably.

anonymous · Answer

hm ok well i did what you said and plugged in numbers before and after zero & both answers were positive. by looking at my graphing calculator it sounds about right (graph is above x axis)

bahrom7893 · Answer

So if they're both positive, the graph looks like this
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