I have the following function f(x, y) =2x2 y + x; which is defined in R² . It shall be evaluated along a path in R² that is a segment of a parabola given by r(t) = ti + t² j for t [0, 2].

1) Determine f and evaluate f at r(1).

2) Determine a tangent vector to r(t) at t = 1.

3) Determine the value s of the directional derivative of f(x, y) at r(1) in the direction (1, 0).

4) Consider the function f evaluated along the segment r(t), that is, f(r(t)). Determinedtdf(r(t)) by use of the chain rule.

5) Find all critical points in t [0, 2] of f along r(t). You do not need to determine the types of the critical points (maxima, minima, inflection points).

6) Isdfdtt=1 different to the value s of the directional derivative at t = 1? Should they be the same?