00:01
Let's find the slope m of the tangent line to the curve y equals 3x squared minus 7x plus 1 at the point 3 .7.
00:09
So first let me write the slope formula which is given by m equals d .y by dx.
00:16
That is the derivative of y with respect to x.
00:20
And since we want to find the slope at the point 3 .7, we evaluate this at the point 3 .1.
00:26
So this equals, we basically have to find the derivative of y with respect to x.
00:33
So if we differentiate this y equation, both sides with respect to x, we will get the derivative of 3x squared is 3 times the derivative of x squared and that is 2x using the power rule of derivatives.
00:48
Then we find the derivative of negative 7x and that is negative 7 times the derivative of x and that is 1 plus the derivative of 1 which is constant is 0.
01:00
And this we have to evaluate at the point 3 comma 1.
01:04
So this equals 3 times 2 x is 6x, negative 7 times 1 is negative 7.
01:11
So let's evaluate this at the point 3 .1.
01:15
And this means we have to replace x by 3 because the point is 3 .1, which means x coordinate is 3.
01:22
So this gives 6 times of 3 minus 7 and this equals 6 times 3 is 18 minus 7 and that equals 11.
01:33
So we found that the slope of the tangent line to the curve at the 0 .3 .7 is 11...
