Minimum value of f (x) = sin x in - π/2 ≤ x ≤ π/2 is
0
1
-1
None of these
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 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 once
Meets the line y = 0 at least twice
Meets the line y = 0 at least thrice
Does not meet the line y = 0
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
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]
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
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 two positive numbers whose sum is 16 and the sum of whose cubes is minimum
8,7
6,8
8,8
8,6
If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f i.e. y = f (x) + ax + b has a relative minimum at x = 0 for
all a and all b
all b if a = 0
all b > 0
all a > 0
The function f (x) = 2x3 - 3x2 - 12x + 4 has
Two maxima
Two minima
One maxima and one minima
No maxima and minima
