P is a point on the parabola f(x) = 1-x^2. A tangent is drawn at point P cuts x axes and y axes to form a triangle. Find the coordinates of P that will minimize the area of the triangle
Hello, pita!
is a point on the parabola:
A tangent is drawn at point cuts x-axis and y-axis to form a triangle.
Find the coordinates of that will minimize the area of the triangle.
The point P has coordinates: .
The derivative is: .
The tangent at has slope: .
The tangent at has the equation: .
. . which simplifies to: .
The area of the triangle is: .
Therefore: . .is the function to be maximized.