The point(s) on the curve $\frac{x^2}{9} + \frac{y^2}{64} = 1$, at which the tangents are parallel to x-axis are

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

Match the LIST-I with LIST-II

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The interval in which the function $f(x)=x^3-12x^2+36x+20$ is increasing, is

Which of the following statements are correct ?

A. The function $f(x) = a^x$ is increasing on $(-\infty,\infty)$ if $a>1$.

B. $f(x) = x^2 - 2x$ is decreasing in $(-\infty,1)$.

C. $f(x) = x(x-3)^2$ increases for $1 \le x \le 3$.

D. $f(x) = e^{-x}$ decreases in $[0,\infty)$.

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Consider the function $f(x) = -2x^3 + 3x^2 + 36x - 15$, then which of the following are TRUE?

A. $f(x)$ increases on $(-2, 3)$

B. $f(x)$ decreases on $(-\infty, -2) \cup (3, \infty)$

C. $f(x)$ increases on $(-\infty, -2) \cup (3, \infty)$

D. $f(x)$ neither increases nor decreases on $(-2, 3)$

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The side of an equilateral triangle is increasing at the rate of 2 cm/sec. The rate at which the area of the triangle is increasing, when the side of the triangle is 5 cm, is