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:
Substitute this condition into the equation of the circle to solve for x, then find y by taking half of x.
Now solve for zeros (or critical numbers to f(x)) then study the sign to determine types of extrema.