The minimum value of the function max (x, x) is equal to

• 0

• 1

• 2

• 1/2

If f(x) = $\sqrt{2\mathrm{x}} + \frac{4}{\sqrt{2\mathrm{x}}}$, then f'(2) is equal to

• 0

• - 1

• 1

• 2

Let f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0. The minimum of f is attained at a point q and the maximum is attained at a point p. If p = q, then a is equal to

• 1

• 3

• 2

• 0

4.

For all rest numbers x and y, it is known as the real valued function f satisfies f(x) + f(y) = f(x + y). If f(1) = 7, then $\sum _{\mathrm{r} = 1}^{100}\mathrm{f}\left(\mathrm{r}\right)$ is equal to

• 7 x 51 x 102

• 6 x 50 x 102

• 7 x 50 x 102

• 7 x 50 x 101

If f(x) = $\left|\begin{array}{ccc}\mathrm{x}& {\mathrm{x}}^2& {\mathrm{x}}^3\\ 1& 2\mathrm{x}& 3{\mathrm{x}}^2\\ 0& 2& 6\mathrm{x}\end{array}\right|$, then f'(x) is equal to

• x³ + 6x²

• 6x³

• 3x

• 6x²

The difference between the maximum and minimum value of of the function $\mathrm{f}\left(\mathrm{x}\right) = {\int }_0^{\mathrm{x}}\left({\mathrm{t}}^2 + \mathrm{t} + 1\right)\mathrm{dt}$ on [2, 3] is

• 39/6

• 49/6

• 59/6

• 69/6

If a and b are the non-zero distinct roots of x² + ax + b = 0, then the minimum value of x² + ax + b is

• 2/3

• 9/4

• - 9/4

• - 2/3

Let f(x + y) = f(x) f(y) and f(x) = 1 + sin(3x) g(x), where g is differentiable.The f'(x) is equal to

• 3f(x)

• g(0)

• f(x)g(0)

• 3g(x)

The roots of the equation $\left|\begin{array}{ccc}\mathrm{x} - 1& 1& 1\\ 1& \mathrm{x} - 1& 1\\ 1& 1& \mathrm{x} - 1\end{array}\right|$ = 0 are

• 1, 2

• - 1, 2

• - 1, - 2

• 1, - 2

$\left|\begin{array}{ccc}1& 1& 1\\ \mathrm{p}& \mathrm{q}& \mathrm{r}\\ \mathrm{p}& \mathrm{q}& \mathrm{r} + 1\end{array}\right|$ is equal to

• q - p

• q + p

• q

• p