Question

in which the sine curve y=c sin (x/a) meets the
is of x is a point of inflexion.
The curve
y = c sin (x/a),​

Answer 1

Answer:

dude please ask your question clearly.

Answer 2

 

Step-by-step explanation:

       The given sine curve is $y=c sin\frac{x}{a}$.

                        $\frac{dy}{dx} =\frac{c}{a} cos \frac{x}{a}$;

                        $\frac{d^{2} y}{dx^{2} } =-\frac{c}{a^{2} } sin \frac{x}{a}$

                        $\frac{d^{3} y}{dx^{3} } =\frac{-c}{a^{3} } cos \frac{x}{a}$

       The given curve meets the x-axis at the point where $y=0$ i.e, $\frac{x}{a}=0$.

                       $\frac{x}{a} =n\pi$; $n$∈Z or $x=n\pi a$; n∈Z.

           Now for $x=n\pi a$,  $\frac{d^{2} y}{dx^{2} } =0$  and $\frac{d^{3} y}{dx^{3} } =\frac{-c}{a^{3} } cos n\pi \neq 0$.

     Where $(an\pi ,0)n$∈Z are the point of inflection for the curve i.e., every point where the curve meets the x-axis is a point of inflection of the curve.