The largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
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 x be real the minimum value of x2 - 8x + 17 is
-1
0
1
2
At x = 5π/6 , f(x) = 2 sin 3x + 3 cos 3x is
Maximum
Minimum
Zero
None of these
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
Given that f (x) = x1/x, x > 0 has the maximum value at x = e, then
eπ > πe
eπ < πe
eπ = πe
eπ ≤ πe
The function f (x) = 2x3 - 3x2 - 12x + 4 has
Two maxima
Two minima
One maxima and one minima
No maxima and minima
The least value of a such that the function x2+ax+1 is increasing on (1,2) is
-2
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]
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
