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Differential Calculus NAT Level - 1 - Question 1

If f"(x) > 0 and f'(1) = 0 such that g(x) = f(cot^{2} x + 2cot x + 2) where 0 < x < π, then g(x) decreasing in (a, b) where is

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Differential Calculus NAT Level - 1 - Question 2

If f(x) has a maximum or a minimum at a point x_{0} inside the interval, then f '(x_{0}) equals :

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Differential Calculus NAT Level - 1 - Question 3

If 1" = α radians, then the approximate value of cos 60°1' is given as Find the value of λ.

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Differential Calculus NAT Level - 1 - Question 4

The maximum value of *u* is, where u = axy^{2}z^{2} - x^{2}y^{2}z^{3} - xy^{3}z^{3} - xy^{2}z^{4} is Find the value of α.

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Differential Calculus NAT Level - 1 - Question 5

The sum of one number and three times a second number is 60. Find the pair, where product is maximum.

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Differential Calculus NAT Level - 1 - Question 6

Let be increasing for all real values of *x*, then range of *a* is (α, ∞). Find value of α.

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Differential Calculus NAT Level - 1 - Question 7

The greatest and the least value of the function f(x) = x^{3} – 18x^{2} + 96x in the interval [0, 9] are :

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Differential Calculus NAT Level - 1 - Question 8

Let f(x, y) = x^{4} + y^{4} - 2x^{2} + 4xy - 2y^{2} has a minimum at (-√α, √α) and (√α, - √α) Find the value of α.

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Differential Calculus NAT Level - 1 - Question 9

If the function is downward concave is (α, β) the [β - α] is

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