Find an equation for the line tangent to the curve at the point defined by the given value of t. also, find the value of d^2y / dx^2 at this point.
x = 3t^2 + 7, y = t^6, t = -1

The tangent line has slope , which we can find using the chain rule:

We have

so that

When , the tangent line has slope 1.

To compute the second derivative , first notice that the first derivative turns out to be a function of . Denote this first derivative by . Then by the chain rule, we find

and at , we get a value of 2/3.

5050

hope this !

the answer is 1030 it's very simple math.