If the normal to the curve y = f(x) at the po | vedclass

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

Question

(D) The slope of the normal to the curve $y = f(x)$ at a point is given by $m_n = 	an(	heta)$,where $	heta$ is the angle the normal makes with the

Vedclass · Accepted Answer

$ 1 $

Vedclass · Answer

(D) The slope of the normal to the curve $y = f(x)$ at a point is given by $m_n = 	an(	heta)$,where $	heta$ is the angle the normal makes with the positive $x$-axis.Given $	heta = \frac{3\pi}{4}$,the slope of the normal is $m_n = 	an\left(\frac{3\pi}{4}ight) = -1$.We know that the slope of the normal is related to the slope of the tangent $(f'(x))$ by the formula $m_n = -\frac{1}{f'(x)}$.At the point $(3, 4)$,the slope of the tangent is $f'(3)$.Therefore,$-1 = -\frac{1}{f'(3)}$.Solving for $f'(3)$,we get $f'(3) = 1$.

If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes an angle $\frac{3\pi}{4}$ with the positive $x$-axis,then $f'(3)$ is equal to

Similar Questions

The instantaneous displacement of a simple pendulum oscillator is given by $x = A \cos \left( \omega t + \frac{\pi}{4} \right)$. Its speed will be maximum at time:

Which one of the following equations is correct for the reaction $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$?

Observe the following statements:
$A$. Three vectors are coplanar if one of them is expressible as a linear combination of the other two.
$R$. Any three coplanar vectors are linearly dependent.
Then,which of the following is true?

The first transgenic plant was tobacco. It contains a resistance gene against which of the following?

Four diatomic species are listed below. Identify the correct order in which the bond order is increasing in them:

Vedclass Test Series

Exam Paper Generator

Online Exam Module