Exercise 23

Let $f$ be the function defined by $f(x,y) = 2x^2+3y^3$.

1. Find the equation of the tangent plane to $f$ at the point $(1,2)$.

2. Use the linearization to approximate the values of $f$ at the points $(1.1, 2.05)$ and $(1.3,2.2)$.

3. Compare the approximations form part (b) to the exact values of $f(1.1, 2.05)$ and $f(1.3, 2.2)$. Which approximation is more accurate. Explain why this should be expected.