# Implicit differentiation, integral, maximum area

Use implicit differentiation to find an equation of the line tangent to the curve x3 + 2xy + y3 = 13 at the point (1, 2).

What is the maximum possible area of a rectangle inscribed in the ellipse x2 + 4y2 = 4 with the sides of the rectangle parallel to the coordinate axes?

3

. Evaluate ∫ dt / (t+1)^2

1

https://brainmass.com/math/integrals/implicit-differentiation-integral-maximum-area-160964

#### Solution Summary

This shows how to use implicit differentiation to find a tangent line, find maximum possible area of a given shape, and evaluate a given integral.

$2.19