Problem 1. (3 points) Given the following functions: f(u) = u?/2 and g(x) = 28 + 1. Find: f' (g(x)) = g'(x) = (fog)'(x) =Problem 2. (5 points) NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for co and '-INF' for -Oo. And use 'U' for the union symbol. Enter DNE if an answer does not exist. f(x) = x' + 3x2 - 20 a) Give the domain of f (in interval notation) b) Find the critical numbers of f. (Separate multiple answers by commas.) C) Determine the intervals on which f is increasing and decreasing. f is increasing on: (Write as a union of intervals if there are more than one). f is decreasing on: (Write as a union of intervals if there are more than one). d) Use the First Derivative Test to determine whether each critical point is a local maximum, minimum, or neither. Local maxima occur at ~ = (Separate multiple answers by commas.) Local minima occur at I (Separate multiple answers by commas.)Problem 3. (3 points) Find an equation of the line tangent to the curve defined by a$ + 4ry + y* = 25 at the point (1, 2).Problem 4. (3 points) The function f(x) = 2 sin(x) +- V3 2 " has two inflection numbers A