The function $f(x) = x^3 - 4x^2 + 4x + 3$ defined on $[-1, 3]$ has

Let $f(x) = \int\limits_0^x \frac{\cos t}{t} dt, x > 0$. Then $f(x)$ has:

The maximum value of $x^4 y^4$ given the constraint $a^2 x^4 + b^2 y^4 = c^6$ is

Let $f(x) = (x - 3)^{2018}(x - 2)^{2019}, x \in R$. If $f(\alpha)$ is a relative maximum of $f$ at $x = \alpha$, then $2\alpha + 3f(\alpha) =$

If $x$ is real,then the minimum value of $\frac{x^2-x+1}{x^2+x+1}$ is

Let $\alpha = \sum_{k=1}^{\infty} \sin^{2k}\left(\frac{\pi}{6}\right)$. Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by $g(x) = 2^{\alpha x} + 2^{\alpha(1-x)}$. Then,which of the following statements is/are $TRUE$?
$(A)$ The minimum value of $g(x)$ is $2^{7/6}$
$(B)$ The maximum value of $g(x)$ is $1 + 2^{1/3}$
$(C)$ The function $g(x)$ attains its maximum at more than one point
$(D)$ The function $g(x)$ attains its minimum at more than one point