Find the maximum or minimum values, if any, without using derivatives,

1.	Find the maximum or minimum values, if any, without using derivatives, of the function:sin 2x+5
Answer» max. value = 4, min. value = 6 f(x) = sin2x+5 We know that, -1≤sinӨ≤1 -1≤sin2x≤1 Adding 5 on both sides, -1+5≤sin2x+5≤1+5 4≤sin2x+5≤6 Hence max value of f(x) = 2x+5 will be 6 Min value of f(x) = 2x+5 will be 4

Find the maximum or minimum values, if any, without using derivatives, of the function:sin 2x+5

Answer»

max. value = 4, min. value = 6

f(x) = sin2x+5

We know that,

-1≤sinӨ≤1

-1≤sin2x≤1

Adding 5 on both sides,

-1+5≤sin2x+5≤1+5

4≤sin2x+5≤6

Hence

max value of f(x) = 2x+5 will be 6

Min value of f(x) = 2x+5 will be 4