f (x) = 1 + [cos x] x, in 0 < x ≤ π/2
Has a maximum value 2
Is continuous in [0, π/2]
Has a minimum value 0
Is not differentiable at x = π/2
Let f (x) satisfy the requirements of Lagrange's Mean Value Theorem in [0, 2].If f (0) = 0 and | f' (x) | ≤ 1/2 for all x in [0, 2], then
f (x) ≤ 2
| f (x) | ≤ 1
f (x) = 2x
f (x) = 3 for at least one x in [0, 2]
At x = 5π/6 , f(x) = 2 sin 3x + 3 cos 3x is
Maximum
Minimum
Zero
None of these
The maximum value of sin x + cos x is
1
2
√2
1/√2
The two positive numbers whose sum is 16 and the sum of whose cubes is minimum
8,7
6,8
8,8
8,6
Two towns A and B are 60 Km apart.A school is to be built to serve 150 students in town A and 50 students in town B.If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at
Town B
45 km. from town A
Town A
45 km. from town B
If a + b + c = 0, then the quadratic equation 3 ax2 + 2 bx + c = 0 has
Imaginary roots
At least one real root in (0, 1)
One root in [2, 3] and other in [3, 6]
For the curve y = xex, the point
x = -1 is a minimum
x = -1 is a maximum
x = 0 is a minimum
x = 0 is a maximum
The function f (x) = x + 4/x has
A local maxima at x = 2 and local minima at x = -2
Local minima at x = 2 and local maxima at x = -2
Absolute maxima at x = 2 and absolute minima at x = -2
Absolute minima at x = 2 and absolute maxima at x = -2
The function f is differentiable with f (1) = 8 and f' (1) = 1/8.If f is invertible and g = f-1, then
g' (1) = 8
g' (1) = 1/8
g' (8) = 8
g' (8) = 1/8