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 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 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
The maximum value of sin x cos x is
1/4
1/2
4
The largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
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
If the graph of a differentiable function y = f (x) meets the lines y = -1 and y = 1, then the graph
Meets the line y = 0 at least twice
Meets the line y = 0 at least once
Meets the line y = 0 at least thrice
Does not meet the line y = 0
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 maximum and minimum value of 3x4-8x3+12x2-48x+1 on the interval [1,4] is
257,-63
-257,63
-63,-63
-40,-40
