Hence, $$f(x)$$ is increasing when $$n \in \left( { - {\pi \over 2},{\pi \over 4}} \right)$$
2
AIEEE 2006
MCQ (Single Correct Answer)
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is
A
$${3 \over 2}{x^2}$$
B
$$\sqrt {{{{x^3}} \over 8}} $$
C
$${1 \over 2}{x^2}$$
D
$$\pi {x^2}$$
Explanation
Area $$ = {1 \over 2}{x^2}\,\sin \,\theta $$
Maximum value of $$\sin \theta $$ is $$1$$ at $$\theta = {\pi \over 2}$$
$${A_{\max }} = {1 \over 2}{x^2}$$
3
AIEEE 2006
MCQ (Single Correct Answer)
The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at