The equation of a line tangent to f at a point b is given by y = f'(b)(x - b) + f(b). So if f = 6 - x^2, then f(1) = 5, f'(1) = -2 and the line is given by y = -2(x - 1) + 5 = -2x + 7. The y-intercept of this line is 7, and the x-intercept is at 7/2. So the area of the triangle is 1/2 * 7 * 7/2 = 49/4 = 12.25.