If the function $f(x) = 2x^2 - kx + 7$, is increasing on $[1,2]$, then $k$ lies in the interval

For $x \in \mathbb{R}$, if $f(x) = -(x-1)^2 + 2$, then

(A) $f$ is an increasing function on $(-\infty, 1]$

(B) $f$ has no critical points

(C) $f$ has a maximum value at $x = 1$

(D) $f$ has a minimum value at $x = 1$

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

The largest interval, in which the function $f(x) = x^3 + 2x^2 - 1$ is increasing, is:

For the function $f(x) = x^{1/x}$, $x > 0$, which of the following are correct?

(A) $x = 0$ is the only point where extremum may occur.

(B) The given function is maximum at $x = e$.

(C) The function has no extreme value for $x > 0$.

(D) The maximum value of the function $f(x)$ is $e^{1/e}$.

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The function $f:R\to R$ is defined by $f(x)=2x^3+5$, then which of the following statements are correct ?

(A) $f(x)$ has no local maximum value.

(B) $f(x)$ has no local minimum value.

(C) $f(x)$ has both local maximum and local minimum values.

(D) $f(x)$ has neither a local maximum value nor a local minimum value

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The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is: