The graph of f '(x) is given in the gure. HINT: Draw and label sign graphs (number lines) to answer the following. Do a number line for the First Derivative Test AND the Second Derivative Test. On what interva|(s) is f [x] concave up? 0 (4, 2) O (1, 00) O (6, 2}, (4, 00} O (009 _4)9 (2100) Enter your answer into the field. Use the format a/b if entering a fraction. Do not put units into the field, they have been provided for you. A construction worker pulls a 5 meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). If the worker is pulling the rope at a rate of 2 meters per second, how fast is the end of the plank sliding along the ground when it is 3 meters from the wall of the building? 2 m / sec 5 m dt m/sBy the Extreme Value Theorem, the given function is guaranteed to have an absolute max and min on a closed interval. Use the the first derivative to find these extreme points. Enter the x and y values of the ordered pairs in the fields below. Determine the absolute extrema for f(x) = x -12x on [0, 4]. Give points as ordered pairs. Absolute Max: Absolute Min:Find the value of "c" {the constant of integration), that would be used to solve the given differential equation. f '(x) = 2(x 1) , f(x) passes through the point (3,2)