00:01
In this question we have given the equation the y is equals to 2x cube minus 3x square minus 15 x plus 1 to find points at which the slope of the tangent of the given equation or you can say the given curve the slope of the tangent of given curve is minus 3.
00:43
So here we begin with the proof clearly dbap by d x is minus 3 which implies that 6x squared minus 6x minus 15 is minus 3 which implies that so here 6x 2 minus 6x 2 minus 6x 2 minus 6x 2 which implies that 6x 2 minus 6x 2 minus 6x minus 6x minus 15 plus 3 is 0 which implies that 6x square minus 6x minus 12 is equals to 0, which implies that 6 into x x squared minus x minus 2 is equal to 0.
01:32
Clearly 6 is not equal to 0 hence this part is 0 which implies that x squared minus x minus 2 is equal to 0 which implies x square minus 2x plus x minus 2 is equal to 0 which implies x into x minus 2 plus x minus 2 is minus 2 is equals to 0 which implies x plus 1 into x minus 2 is 0 which implies x is either minus 1 or 2 the value of x is 2.
02:08
For these values now we will find out the values of y.
02:14
Clearly the value of x is minus 1 and 2.
02:21
The value of x is minus 1 and the value of x is 2.
02:29
We have clearly the equation given y is equal to 2 x q minus 3 x square minus 15 x plus y.
02:39
Substituting the value first of all y is equal x is equals to 2.
02:44
2 multiplied by 8 minus 3 into 4 minus 15 multiplied by 2 plus 1 which states that y is minus 25...