Question

1. Find the absolute maximum and minimum values of the function sin 2x + 5.

2. If 0<x<2π, find the maximum and minimum values of the function f(x)= x + sin 2x.​

Answer 1

Answer:

Finding Absolute Extrema of f(x) on [a,b]

Verify that the function is continuous on the interval [a,b] .

Find all critical points of f(x) that are in the interval [a,b] . ...

Evaluate the function at the critical points found in step 1 and the end points.

Identify the absolute extrema.

Answer 2

Answer:

Ex 6.5,12 Find the maximum and minimum values of x + sin 2x on [0, 2π ] Let ... f'(x)=d(x + sin 2x)/dx =1+2 cos⁡2x Putting f'(x)=0 1 + 2 cos 2x=0 2 ...