The function $f(x) = x^3 + 2x^2 - 1$ is

(A) increasing in $\left(\dfrac{-4}{3}, 0\right)$

(B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$

(C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$

(D) increasing in $(0, \infty)$

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The rate of change of the area of a circle with respect to its radius $r$, when $r = 3$cm, is:

The ordinate of the point on the curve $y^2 = 8x$ for which abscissa and ordinate change at the same rate is:

Which of the following are correct?

(A) The function $f(x) = 3x+12$ is increasing on R.

(B) The function $f(x) = e^{2x}$ is decreasing on R.

(C) The function $f(x) = x^2-x-1$ is neither increasing nor decreasing on (-1, 1).

(D) The function $f(x) = x^3-3x^2+4x$ is increasing on R.

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Based on above information answer the following question :

If area of the flower bed is maximum, then area (in $m^2$) of the garden, which is outside the flower bed is :

For the function, $f(x) = \frac{-3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 - 350$, which of the following statements are correct?

(A) $x = -3$ and $x = -5$ are the only critical points of the given function.

(B) $x = -3$ is a point of local minimum.

(C) The local minimum value at $x = -3$ is 23.1.

(D) $x = -5$ is a point of local maximum.

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The semi vertical angle of a right circular cone of maximum volume of a given slant height is