The two positive numbers whose sum is 16 and the sum of whose cubes is minimum
8,7
6,8
8,8
8,6
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]
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) = 2x3 - 3x2 - 12x + 4 has
Two maxima
Two minima
One maxima and One minima
No maxima and minima
The maximum value of sin x cos x is
1/4
1/2
4
If x be real the minimum value of x2 - 8x + 17 is
0
The maximum value of sin x + cos x is
√2
1/√2
The largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
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
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
