Question

For the shown graph the slope of graph from point A to point B:

• A. Continuously decreases
• B. Continuously increases
• C. First increases then decreases
• D. First decreases then increases

Answer 1

The correct option is A Continuously decreases

$\left(A\right)$

Slope of the graph = tangent of angle made by tangent with +x axis

From $A\to C$ : $\theta$ is acute and decreases $\Rightarrow$ slope decrease

From $C\to B$ : $\theta$ is obtuse and decreases $\Rightarrow$ slope decreases

Explanation of variation: Let $s=tan\theta$

$ds=se{c}^2\theta d\theta$

since $se{c}^2\theta \ge 0$(non negative)

so $d\theta$ decides sign of $ds$

and since $d\theta$ is negative in both case $\Rightarrow$$ds$ is negative

so slope decreases continously