Find the coordinates of the point p on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by the tangent line at p, the x-axis, and y-axis

Let point P be with coordinates Find the equation of the  tangent line.

1. If then

2. The equation of the tangent line at point P is

Find x-intercept and y-intercept of this line:

The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

Since point P is on the parabola, then and

Find the derivative A':

Equate this derivative to 0, then

And

two points:

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15