Question

Find the local minimum value of the function f(x) = sin⁴x + cos⁴x, 0 < x < π2
(a) 1√2
(b) 1/2
(c) √3/2
(d) 0​

Answer 1

Step-by-step explanation:

Let f(x)=cos

4

x+sin

4

x

=(cos

2

x)

2

+(sin

2

x)

2

=(cos

2

x+sin

2

x)

2

−2sin

2

xcos

2

x.................[a

2

+b

2

=(a+b)

2

−2ab]

=1−

2

(sin2x)

2

for max value of f(x),sin2x=0

f(x)=1−0=1

for min. value of f(x),sinx=1 or −1

f(x)=1−

2

1

=

2

1