00:01
The question says that a point 3 comma 2 is on a curve and the slope of the tangent at point x y to the curve is given by this equation to x minus 3.
00:10
We need to find out the equation of the curve.
00:13
Okay.
00:14
So i will consider that the equation of the curve, so let the equation of the curve, let it be y equal to f of x.
00:29
So this implies that slope of tangent at any point x y to this curve it is given by derivative of the curve with respect to x okay.
00:45
So this will implies that d y by d x and slope is given to be how much it is twice of x minus three.
00:53
So if i rearrange i will get d y equals to 2x minus 3 times of d x okay.
00:59
So integrating both sides, so integrating both sides, what we are going to get, integral of d .y is equal to integral of twice of x minus three times dx.
01:19
So this implies that y is equal to take the derivative integral to x squared divided by 2 minus 3x plus the constant of integration, correct? so this will give me what this will give me y is equal to x square minus 3x plus c okay since 3 comma 2 lies on the curve okay so you have to just put put x equal to 3 y equal to 2 let's say in equation 1 and let's say this is the equation 1 so if i put i will get the value of c easily.
02:03
So this will imply that y, that is 2 and x square becomes 9 3 times 3...