about applications of derivatives. Which kind of application did you find the most interesting or most relevant to your program of study? Explain why you chose the application you did. 1. Locate the critical points for f(x)= x3 + 21x. Then use the First Derivative Test to determine whether they correspond to local maxima or local minima. 2. Find the interval(s) on which g(x) = 3x4 42%2 + 10); + 24 is concave up and interval(s) on which it is concave down. Justify your answers using the second derivative of g. 4 3. Find the absolute maximum and minimum values off(x) = (x 4)? in the interval [-1, 31]. Locate where each of these extreme values occur in the given interval. 4. - Letf(x) = Ex} 3x2 + 12;: on the closed interval [-1, 8]. Locate any critical points forfwithin the given interval. 5 Find the interval(s) on which f(x) x3 + 12):\" + 50 is increasing and the interval(s) on which it is decreasing Justify your answers using the first derivative off. 6. Consider the functionf(x) = x+5A At what point(s) in the interval [0,2] is the instantaneous rate of change equal to the average rate of change, as guaranteed by the Mean Value Theorem? 7. Explain why x): |x 1 | does not satisfy the conditions of the Mean Value Theorem on the interval [- -2 2]. 8 Graph an example of a function which is both increasing and concave up through the entire interval 0