Question

Find max and min value:
y= sin²((π/4)-x)+(sinx-cosx)²

Answer 1

To find the maximum and minimum values of the given function, we need to find the critical points by setting the derivative equal to zero. Then, we can determine the maximum and minimum values by plugging these critical points back into the original function.

Step-by-step explanation:

To find the maximum and minimum values of the function y = sin²((π/4)-x)+(sinx-cosx)², we need to determine the critical points by finding where the derivative is equal to zero.

The derivative of the function is y' = -2sin((π/4)-x)cos((π/4)-x) + 2(sin(x)-cos(x))(cos(x)+sin(x)).

Setting this derivative equal to zero and solving for x, we get the critical points.

Then, we can plug these critical points back into the original function to find the corresponding y-values to determine the maximum and minimum values.