Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1, –1, 1) and at (–1, –1, 1) to z = 3 – x^2 – y^2

Let F(x, y) = <3x?y3 + y", 3x°y² + y^ + 4xy³,. %3D Evaluate F.dr where C is the line segment from (1, 2) to (-2, 1).

Let vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.

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.