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 largest interval for which x12 - x9 + x4 - x + 1 > 0 is
-4 < x ≤ 0
0 < x < 1
-100 < x < 100
-∞ < x < ∞
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
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
Minimum value of f (x) = sin x in - π/2 ≤ x ≤ π/2 is
0
1
-1
None of these
At x = 5π/6 , f(x) = 2 sin 3x + 3 cos 3x is
Maximum
Minimum
Zero
The least value of a such that the function x2+ax+1 is increasing on (1,2) is
2
-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]
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
Given that f (x) = x1/x, x > 0 has the maximum value at x = e, then
eπ > πe
eπ < πe
eπ = πe
eπ ≤ πe
