(s) Find the linearization of f at the given point. Then estimate the value of f. (a) f(x, y) = xy² at (2, 1). Estimate f(2.001, 1.05) y? f(x, y) = at (1,2). Estimate f(0.99, 1.99)

Consider the function f(x) = ax³ + bx where a > 0. (a) Consider b > 0. i. Find the x-intercepts. ii. Find the intervals on which f is increasing and decreasing. iii. Identify any local extrema. iv. Find the intervals on which f is concave up and concave down. (b) Consider b < 0. i. Find the x-intercepts. ii. Find the intervals on which f is increasing and decreasing. iii. Identify any local extrema. iv. Find the intervals on which f is concave up and concave down.

Find the linear approximation of the function below at the indicated point. f(x, y) = In(x - 2y) at (3, 1) f(x, y) = Use the approximation to find f(2.92, 1.04). Illustrate by graphing f and the tangent plane. f(2.92, 1.04) *

Calculate the range of f(x,y) using this equation f(x,y)=2x2+y2+1 and the given figure.