Applications of Derivatives

Calculus

Find the Area of the Largest Rectangle That Can Be Inscribed in the Ellipse x²/a² + y²/b² = 1 With Its Sides Parallel to the Coordinate Axes
ByShiwam October 9, 2026September 16, 2026

Find the maximum area of a rectangle inscribed in the ellipse x²/a²+y²/b²=1, using the parametric point (a cosθ, b sinθ) and maximising over θ.

Read More Find the Area of the Largest Rectangle That Can Be Inscribed in the Ellipse x²/a² + y²/b² = 1 With Its Sides Parallel to the Coordinate Axes
Calculus

The Tangents to the Curve y = (x−2)² − 1 at Its Points of Intersection With the Line x − y = 3 Intersect at the Point
ByShiwam September 29, 2026September 16, 2026

Find where the tangents to y=(x−2)²−1 at its points of intersection with the line x−y=3 meet, by finding the two intersection points, their slopes, and solving the tangent-line system.

Read More The Tangents to the Curve y = (x−2)² − 1 at Its Points of Intersection With the Line x − y = 3 Intersect at the Point