The function f(x) = 2x - 33x + 144x The smaller one is x = and the larger one is x = 7 has two critical numbers. Consider the function f(x) = 4 - 5x, -4 x 2. The absolute maximum value is and this occurs at x = The absolute minimum value is and this occurs at x = The function f(x) 2x + 30x This function has a local minimum at x = with value - and a local maximum at x = with value 96x + 8 has one local minimum and one local maximum. Homework 2.7 Score: 0/7 0/7 answered Question 4 Given the function g(x) = 8x + 12x 144x, find the first derivative, g'(x). g'(x) = Notice that g'(x) 0 when x = 2, that is, g'(2) = 0. Now, we want to know whether there is a local minimum or local maximum at x 2, so we will use the second derivative test. Find the second derivative, g''(x). g''(x) = Evaluate g"(2). g'' (2) = < > Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 2? [Answer either up or down -- watch your spelling!!] At x 2 the graph of g(x) is concave Based on the concavity of g(x) at x = 2, does this mean that there is a local minimum or local maximum at x = 2? [Answer either minimum or maximum -- watch your spelling!!] At x = 2 there is a local Question Help: Video Submit Question Homework 2.7 Score: 0/7 0/7 answered Question 5 -5 -4 -3 -2 -1 3 2 -2 < > The above is the graph of the derivative f '(x). How many critical points does the original function f(x) have? Question Help: Video 1 Video 2 Submit Question