Find the absolute max. and min. of each function

Question

y=√4−x^2, (−2,1)

f (theta)= sin theta, {-∏/2, 5∏/6}

f(x)= 1/x + In x, [1/2, 4]

Answer 1

For these, put the end points into the function and save the results.

Take the derivative of the function, set it to zero and solve for the independent variable. Then find the function value for that variable.

Sort all the results from minimum to maximum values.

The least is the absolute minimum and the most is the absolute maximum.

For the first one,

y = f(x) = √4-x²

f(-2) = -2

f(1)=1

f'(x) = -2x

-2x=0 --> x=0 --> f(0) = 2

-2

1

2

Abs min = -2

Abs max = 2

Do the same for the other two functions