Question

for the curve y=f(x) let m is the slope of normal at x1y1 then slope of normal is​

Answer 1

Tangents and Normals

The given curve is y = f(x)

The equation of the normal at any point $(x_{1},\:y_{1})$ on the given curve is

$\quad (y-y_{1})=-\frac{1}{(f'(x))_{(x_{1},\:y_{1})}}(x-x_{1})$

$\Rightarrow (f'(x))_{(x_{1},\:y_{1})}(y-y_{1})+(x-x_{1})=0$

provided $f'(x)$ exists infinitely.

However we have found:

$\quad m=-\frac{1}{(f'(x))_{(x_{1},\:y_{1})}}$

This is the required slope of normal to the given curve.

Note:

1. When the curve $y=f(x)$ is given and we have to find its tangent at any point $(\alpha,\:\beta)$, find derivative $\frac{dy}{dx}$ at that point, as it gives the slope of the tangent at that point.
2. To find the normal at that point, find derivative $(-\frac{dx}{dy})$ at that point, as it gives the slope of the normal at that point.

Answer 2

Step-by-step explanation:

What is the equation of normal for the curve y=f(x) at the point (x1,y1)