The function f (x) = 2x3 - 3x2 - 12x + 4 has
Two maxima
Two minima
One maxima and one minima
No maxima and minima
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
The maximum value of sin x cos x is
1/4
1/2
1
2
The least value of a such that the function x2+ax+1 is increasing on (1,2) is
-2
-1
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]
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
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 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 maximum and minimum value of 3x4-8x3+12x2-48x+1 on the interval [1,4] is
257,-63
-257,63
-63,-63
-40,-40
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
