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
f (x) = 1 + [cos x] x, in 0 < x ≤ π/2
is continuous in [0, π/2]
has a maximum value 2
has a minimum value 0
is not differentiable at x = π/2
Given that f (x) = x1/x, x > 0 has the maximum value at x = e, then
eπ > πe
eπ < πe
eπ = πe
eπ ≤ πe
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 least value of a such that the function x2+ax+1 is increasing on (1,2) is
2
-2
1
-1
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
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]
None of these
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
Minimum value of f (x) = sin x in - π/2 ≤ x ≤ π/2 is
0
The largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
