00:01
And this question, which of the following is the equation of the tangent line to this particular curve at x equal to minus 1? so the tangent line is y is equal to 2 minus x square times x cube.
00:14
For the tangent line, first we need to find the coordinate.
00:17
So x is already given to minus 1 as minus 1.
00:21
So what is the corresponding y coordinate? that will be 2 minus minus 1 whole square whole cube.
00:26
So that will be 2 minus 1 because minus 1 square is 1 and 2 minus 1 is 1.
00:30
So that will become one cube, which is just one.
00:33
So that will be minus one one.
00:36
And then we find the derivative.
00:38
So dy over dx will be three comes down.
00:42
We have two minus x square whole square.
00:44
And then inside is d over dx of two minus x square.
00:49
So that will become three times two minus x square whole square.
00:53
And the derivative of this following function is going to be zero minus two x using the chain rule or power chain rule.
01:01
So 0 minus 2x is minus 2x and 3 times minus 2x is minus 6x.
01:05
So that will be minus 6x times 2 minus x square whole square.
01:09
That is the value of dy over dx.
01:12
So the value of dy over dx at x equal to minus 1 because that's what we have to find the slope.
01:18
So dy over dx at x equal to minus 1 is going to be negative 6 times minus 1.
01:24
And then 2 minus 1 is 1...