Question

y=3sinx+sin^2(x)
find the maximum and minimum values

Answer 1

apparently the max is 4 and the min in -2
maybe we can take the derivative and find the critical points

Answer 2

actually that is unnecessary forget i mentioned it

Answer 3

biggest
\[3\sin(x)\] can be is 3, since
\[-1\leq\sin(x)\leq 1\] and similarly the smallest it can be is -3

Answer 4

likewise the largest
\[\sin^2(x)\] can be is also 1

Answer 5

max/min values occur at x = pi/2 and 3pi/2. To find the actual values, stick these x values into the original equation.

Answer 6

so largest
\[3\sin(x)+\sin^2(x)\] can be is 4

Answer 7

minimum occurs when
\[\sin(x)=-1\] meaning
\[3\sin(x)=-3\] and
\[sin^2(x)=1\] so minimum is -2

Answer 8

you can use calculus if you like, but thinking also works for this question, no calc needed

Answer 9

With calculus
y=3sinx+sin^2(x)
at stationary point y'=0
y'=2 sin(x)+3) cos(x)=0

Answer 10

the derivative is
y'=3cosx+2sinxcosx

Answer 11

don't forget the chain rule...

Answer 12

yh, my bad y'=(2 sin(x)+3) cos(x)

Answer 13

y'=(2 sin(x)+3) cos(x)=0