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A function is said to be continuous for x ∈ R, if ____________.
Concept: undefined >> undefined
Find all the points of local maxima and local minima of the function f(x) = (x - 1)3 (x + 1)2
Concept: undefined >> undefined
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Find the local minimum value of the function f(x) `= "sin"^4" x + cos"^4 "x", 0 < "x" < pi/2`
Concept: undefined >> undefined
Find the points of local maxima and local minima respectively for the function f(x) = sin 2x - x, where `-pi/2 le "x" le pi/2`
Concept: undefined >> undefined
If y `= "ax - b"/(("x" - 1)("x" - 4))` has a turning point P(2, -1), then find the value of a and b respectively.
Concept: undefined >> undefined
Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2.
Concept: undefined >> undefined
If y = x3 + x2 + x + 1, then y ____________.
Concept: undefined >> undefined
Find both the maximum and minimum values respectively of 3x4 - 8x3 + 12x2 - 48x + 1 on the interval [1, 4].
Concept: undefined >> undefined
The function f(x) = x5 - 5x4 + 5x3 - 1 has ____________.
Concept: undefined >> undefined
Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.
Concept: undefined >> undefined
Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.
Concept: undefined >> undefined
The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is ____________.
Concept: undefined >> undefined
Find the area of the largest isosceles triangle having a perimeter of 18 meters.
Concept: undefined >> undefined
The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are ____________.
Concept: undefined >> undefined
The distance of that point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x - 1 is ____________.
Concept: undefined >> undefined
The function `"f"("x") = "x" + 4/"x"` has ____________.
Concept: undefined >> undefined
The combined resistance R of two resistors R1 and R2 (R1, R2 > 0) is given by `1/"R" = 1/"R"_1 + 1/"R"_2`. If R1 + R2 = C (a constant), then maximum resistance R is obtained if ____________.
Concept: undefined >> undefined
Let f(x) = 1 + 2x2 + 22x4 + …… + 210x20. Then f (x) has ____________.
Concept: undefined >> undefined
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is a spade’
F : ‘the card drawn is an ace’
Concept: undefined >> undefined
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is black’
F : ‘the card drawn is a king’
Concept: undefined >> undefined
