The interval in which the function $f(x) = x^2 - 3x + 7$ is increasing, is

A car is moving along the curve $y = x^3 + 12$. The point(s) on the curve at which the rate of change of its y-coordinate at a certain time is 3 times the rate of change of its x-coordinate is/are

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing is -

The function $f: R \rightarrow R$ (where $R$ is set of real numbers) defined as

$f(x) = x^2 + 2x$ is

The length of a rectangle is decreasing at 4 cm/minute and the width is increasing at 3 cm/minute. The rate of change of area when length is 10cm and width is 6cm, is:

The cost function of a product is given by $C(x)=\frac{1}{3}x^3-45x^2-900x+36$, where x is the number of units produced. In order to minimize the marginal cost, how many units of the product must be produced?

The function $f(x) = \sin 3x$, $x \in \left[0, \frac{\pi}{2}\right]$

(A) is increasing on $\left[0, \frac{\pi}{6}\right]$

(B) is decreasing on $\left[\frac{\pi}{6}, \frac{\pi}{2}\right]$

(C) is increasing on $\left[0, \frac{\pi}{2}\right]$

(D) is decreasing on $\left[0, \frac{\pi}{2}\right]$

Choose the correct answer from the options given below: