In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?

The interval in which the function given by $f(x) = x^2 e^{-x}$ is strictly increasing is:

Let $f(x) = 4x^3 - 18x^2 + 27x - 5$, $x \in R$. Then which of the following statements are TRUE?

(A) $f''(x) = 24x - 36$

(B) f has local maxima at $x = \frac{3}{2}$ but no minima

(C) f has neither maxima nor minima

(D) f has both maxima and minima

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Match List-I with List-II

The function $f(x) = (x - 1)(x + 1)^2$ has

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The slope of the tangent to the curve $y = 3x^2 + 2kx - 5$ at $x=1$ is $9$. The value of $k$ is :

The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

The function $f(x) = x^2 - 4x + 6$ is

(A) Strictly decreasing on $(-\infty, 2) \cup (2, \infty)$

(B) Strictly increasing on $(2, \infty)$

(C) Strictly increasing on $(-\infty, \infty)$

(D) Strictly decreasing on $(-\infty, 2)$

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