max and min help?

Question

Within the interval (-0.93,4.77), for what value of x does f(x) take on a minimum if

f(x)=3.2sin(1.1x)+5.3cos(1.1x)

Minimum value of f(x) occurs at x=

What is the value of f(x) at this value of x ?

Within the interval ( -0.93,4.77 ), for what value of x does f(x) take on a maximum if

f(x)=3.2sin(1.1x)+5.3cos(1.1x)

Maximum value of f(x) occurs at

What is the value of f(x) at this value of x ?

Answer 1

Take the derivative of the function and equate to 0. Solve for x critical

3.2*1.1*cos(1.1x) - 5.3*1.1*sin(1.1x) = 0 which leads to

(1/1.1)tan^-1(3.2/5.3) = x

Because the inverse tan function has a range of -pi/2 to pi/2. you need to solve for all x in the interval

The second critical x : (1/1.1)(tan^-1(3.2/5.3)+π) = x

one is a max and the other a min.