What is the behavior of the magnitude of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The slope of a graph at any point is given by $	an 	heta$,where $	heta$ is the angle the tangent at that point makes with the positive $x$-axis

Vedclass · Accepted Answer

First decreases then increases

Vedclass · Answer

(A) The slope of a graph at any point is given by $	an 	heta$,where $	heta$ is the angle the tangent at that point makes with the positive $x$-axis.$1$. From $A$ to $B$: The tangent makes an acute angle with the $x$-axis. As we move from $A$ to $B$,the angle $	heta$ decreases from a positive value towards $0$ at the peak $B$. Since $	an 	heta$ is positive and decreasing in this interval,the magnitude of the slope decreases.$2$. At point $B$: The tangent is horizontal,so $	heta = 0^\circ$ and the slope is $0$.$3$. From $B$ to $C$: The tangent makes an obtuse angle with the $x$-axis. As we move from $B$ to $C$,the angle $	heta$ increases from $0^\circ$ towards $90^\circ$. The slope $(	an 	heta)$ is negative,but its magnitude $|	an 	heta|$ increases as the angle becomes more obtuse.Therefore,the magnitude of the slope first decreases (from $A$ to $B$) and then increases (from $B$ to $C$).The correct option is $A$.

What is the behavior of the magnitude of the slope of the shown graph?

Similar Questions

The side of a square is increasing at the rate of $0.2\,cm/s$. The rate of increase of perimeter with respect to time is $...........\,cm/s$.

The value of $\frac{d^2}{dx^2} (4x^3 - 3x^2 + 2x + 1)$ is ..... (in $x - 6$)

If $\tan \theta = \frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant,the value of $\cos \theta$ is

The slope of the graph as shown in the figure at points $1, 2$ and $3$ is $m_1, m_2$ and $m_3$ respectively. Then:

$\frac{d}{dx} {\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)}^2$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module