The function sin⁴ x + cos⁴ x is increasing in the interval

(a)

\(\left[ \frac { 5\pi }{ 8 } ,\frac { 3\pi }{ 4 } \right] \)

(b)

\(\left[ \frac { \pi }{ 2 } ,\frac { 5\pi }{ 8 } \right] \)

(c)

\(\left[ \frac { \pi }{ 4 } ,\frac { \pi }{ 2 } \right] \)

(d)

\(\left[ 0,\frac { \pi }{ 4 } \right] \)

The number given by the Rolle's theorem for the functlon x³ - 3x², x ∈ [0, 3] is

(a)

1

(b)

\(\sqrt { 2 } \)

(c)

\(\frac { 3 }{ 2 } \)

(d)

2

The number given by the Mean value theorem for the function \(\frac { 1 }{ x } \), x ∈ [1, 9] is

(a)

2

(b)

2.5

(c)

3

(d)

3.5

One of the closest points on the curve x² - y² = 4 to the point (6, 0) is

(a)

(2,0)

(b)

\(\left( \sqrt { 5 } ,1 \right) \)

(c)

\(\left( 3,\sqrt { 5 } \right) \)

(d)

\(\left( \sqrt { 13 } ,-\sqrt { 3 } \right) \)

The maximum product of two positive numbers, when their sum of the squares is 200, is

(a)

100

(b)

\(25\sqrt { 7 } \)

(c)

28

(d)

\(24\sqrt { 14 } \)