f (x) = 1 + [cos x] x, in 0 < x ≤ π/2
Has a maximum value 2
Is continuous in [0, π/2]
Has a minimum value 0
Is not differentiable at x = π/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 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
At x = 5π/6 , f(x) = 2 sin 3x + 3 cos 3x is
Maximum
Minimum
Zero
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 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
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
The least value of a such that the function x2+ ax +1 is increasing on (1,2) is
2
-2
1
-1
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
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]
