f'(x)= - sinx - cosx;.........to find extrema, set this equal to zero
- sin x - cosx = 0............sinx = - cosx
Sine and Cosine only have the same values at a reference angle of pi/4; they differ in sign in quadrants II and IV. So the values you are looking at are 3pi/4 and 7pi/4.
Which is a maximum and which is a minimum?
f''(x) = -cosx + sinx
f''(3pi/4) = positive, so 3pi/4 is a minimum; f''(7pi/4) = negative, so 7pi/4 is a maximum
Sin²(x) + 2Sin(x)Cos(x) = 0 element Sin(x)(Sin(x) + 2Cos(x)) = 0 So the two Sin(x) = 0 or Sin(x) + 2Cos(x) = 0 Sin(x) = 0 has strategies x = 0 + n?, the place n is an integer Sin(x) + 2Cos(x) = 0 ? Sin(x) = -2Cos(x) or Sin(x)/Cos(x) = Tan(x) = -2 So x = ArcTan(-2) = -a million.107… + n? the place n is an integer. verify this result interior the unique equation(s), I did!
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First find f'(x).
f'(x)= - sinx - cosx;.........to find extrema, set this equal to zero
- sin x - cosx = 0............sinx = - cosx
Sine and Cosine only have the same values at a reference angle of pi/4; they differ in sign in quadrants II and IV. So the values you are looking at are 3pi/4 and 7pi/4.
Which is a maximum and which is a minimum?
f''(x) = -cosx + sinx
f''(3pi/4) = positive, so 3pi/4 is a minimum; f''(7pi/4) = negative, so 7pi/4 is a maximum
Sin²(x) + 2Sin(x)Cos(x) = 0 element Sin(x)(Sin(x) + 2Cos(x)) = 0 So the two Sin(x) = 0 or Sin(x) + 2Cos(x) = 0 Sin(x) = 0 has strategies x = 0 + n?, the place n is an integer Sin(x) + 2Cos(x) = 0 ? Sin(x) = -2Cos(x) or Sin(x)/Cos(x) = Tan(x) = -2 So x = ArcTan(-2) = -a million.107… + n? the place n is an integer. verify this result interior the unique equation(s), I did!