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
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
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
If y = a log x + bx2 + x has its extremum value at x = -1 and x = 2, then
a = 2, b = -1
a = 2, b = -1/2
a = -2, b = 1/2
None of these
The maximum value of sin x cos x is
1/4
1/2
1
2
The maximum and minimum value of 3x4-8x3+12x2-48x+1 on the interval [1,4] is
257,-63
-257,63
-63,-63
-40,-40
Minimum value of f (x) = sin x in - π/2 ≤ x ≤ π/2 is
0
-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
The largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
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]