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

A balloon which always remains spherical, has a variable diameter $\frac{3}{2}(5x+7)$. Then the rate of change of its volume with respect to x is

The number of tangents to the curve $xy - 3y + 2 = 0$ having slope 2 is:

The maximum value of $\left(\frac{1}{x}\right)^x$ for $x > 0$ is

The real valued function $f(x) = x^{15} + 5x^9 + 10$ is increasing for___________.

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

Choose the correct answer from the options given below:

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is: