The number of turning points of the curve $f(x) = 2 \cos x - \sin 2x$ in the interval $[-\pi, \pi]$ is

Let $f: R \rightarrow R$ be a function defined by $f(x) = (x - 3)^{n_{1}}(x - 5)^{n_{2}}$,where $n_{1}, n_{2} \in N$. Which of the following is $\text{NOT}$ true?

The maximum area of a rectangle inscribed in a circle of radius $10 \text{ cm}$ is

The greatest value of the function $f(x) = -1 + \frac{2}{2^{x^2} + 1}$ is:

For every twice differentiable function $f : R \rightarrow [-2, 2]$ with $(f(0))^2 + (f'(0))^2 = 85$,which of the following statement$(s)$ is (are) $TRUE$?
$(A)$ There exist $r, s \in R$,where $r < s$,such that $f$ is one-one on the open interval $(r, s)$.
$(B)$ There exists $x_0 \in (-4, 0)$ such that $|f'(x_0)| \leq 1$.
$(C)$ $\lim_{x \rightarrow \infty} f(x) = 1$.
$(D)$ There exists $a \in (-4, 4)$ such that $f(a) + f''(a) = 0$ and $f'(a) \neq 0$.

If $f(x) = (\sin^4 x + \cos^4 x)$,$0 < x < \frac{\pi}{2}$,then the function has a minimum value of $ . . . . . . $ at $x = . . . . . . $.