QuestionB. What is the direction of variation of each of the following functions: (co be done by students) 1) $f(x)=\cos x$ for $0 \leq x$ 2) $x(x) \frac{x^{3}+1}{x-1}$ on its domaln of definition 3) $h(x)=\sqrt{x}$ on its domain of definition

Studdy Solution
To determine the direction of variation for $h(x) = \sqrt{x}$, find its derivative:
$$h'(x) = \frac{1}{2\sqrt{x}}$$
Since $h'(x) > 0$ for all $x > 0$, $h(x)$ is increasing on its domain.
The direction of variation for each function is as follows:
1. $f(x) = \cos x$ is decreasing for $0 \leq x < \pi$ and increasing for $x > \pi$.
2. $g(x) = \frac{x^3 + 1}{x - 1}$ varies based on the sign of $g'(x)$ over its domain, excluding $x = 1$.
3. $h(x) = \sqrt{x}$ is increasing on its domain $x > 0$.