Question

hi guys....
good morning



maximum and minimum value of
2 sin² x - 3 sin x +2 is.....
also give proper explanation...

50 points..​

Answer 1

Hola mate

✍️✍️Answer:-

You probably mean the minimum and maximum value of 2 sin^2 (x) - 3 sinx + 2.

Let y = 2 sin^2 (x) - 3 sinx + 2

For y to be minimum or maximum,

dy/dx = 0

Or, 4 sinx cosx - 3 cosx = 0

Or, cosx (4 sinx - 3) = 0

cosx = 0, sinx = 3/4

x = 90°, 48.59°.

d^2 y / dx^2

= 4 (cos^2 (x) - sin^2 (x)) + 3 sinx

= 4 cos (2x) + 3 sinx

When x = 90°, d^2 y / dx^2 = -1 < 0

So, y is maximum when x = 90°

When x = 48.59°, d^2 y / dx^2 = 1.75 > 0

So, y is minimum when x = 48.59°

y (max) = 2 sin^2 (90°) - 3 sin (90°) + 2

= 1

y (min) = 2 sin^2 (48.59°) - 3 sin (48.59°) + 2 = 0.875

Answer 2

hi mate,

solution: Here the minimum and maximum value of 2 sin^2 (x) - 3 sinx + 2.

Let y = 2 sin^2 (x) - 3 sinx + 2

so, For y to be minimum or maximum,

dy/dx = 0

Or, 4 sinx cosx - 3 cosx = 0

Or, cosx (4 sinx - 3) = 0

cosx = 0, sinx = 3/4

x = 90°, 48.59°.

d^2 y / dx^2

= 4 (cos^2 (x) - sin^2 (x)) + 3 sinx

= 4 cos (2x) + 3 sinx

When x = 90°, d^2 y / dx^2 = -1 < 0

So, y is maximum when x = 90°

When x = 48.59°, d^2 y / dx^2 = 1.75 > 0

So, y is minimum when x = 48.59°

y (max) = 2 sin^2 (90°) - 3 sin (90°) + 2

= 1

y (min) = 2 sin^2 (48.59°) - 3 sin (48.59°) + 2 = 0.875

i hope it helps you...