Compute F. dr, where F(x, y) = (Use symbolic notation and fractions where needed.) [F.a с (³+1, 2+1,7) and C is parametrized by r(t) = : (t³, 2, t² ) for 0 ≤ t ≤ 1. F. dr =

Let P be the tangent plane to the graph of g(x, y) = 16 – 8x² – 16y² at the point (4,2,-176). Let f(x, y) = 16 – x² − y². Find the point on the graph of f where the tangent plane is parallel to P. (Use symbolic notation and fractions where needed. Give your answer in the form (*,*,*)).

Use the product rule to derive

4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and determine where each are 0 and/or do not exist (DNE). If none, write "none". f' = 0: f' DNE: f" = 0: f" DNE: c) E Do a sign analysis on f' and f". d) Find the intervals on which f is increasing and decreasing. Increasing: Decreasing: e) Find the intervals on which f is concave up and concave down. Concave up: Concave down: f) answers as (x, y) points. Find all local maxima, local minima, and inflection points of f. Be sure to write your Local max: Local min: Inflection point(s): -4 -3 -1 g) Sketch the graph of f.

Let S be the surface in R' defined by the equation x · y' – 4z = 9. Find a real-valued function g (x, y) of two variables such that S is the graph of g. (Express numbers in exact form. Use symbolic notation and fractions where needed.) g (x, y) =

Do part b in detail