2.

First find a slope form for the given circle by implicitly differentiating with respect to x:

and solve for y':

Because the slopes are equal, the derivative form above, when evaluated at the point of tangency, should be equal to the slope of the given line, which is is -2. Note:

which means

Substitute this condition into the equation of the circle to solve for x, then find y by taking half of x.

1.y=16x+4x^2-x^4

Differentiate

Now solve for zeros (or critical numbers to f(x)) then study the sign to determine types of extrema.

Good luck!!