Please solve these question in details and gully explaination.

Question 6.2 (15 minutes) Determine if the following statements are true or false. If a statement is true explain why. If it is false, then give an example of a function that demonstrates that the statement is false. Discuss with someone at another table and arrive at consensus. 1. For all functions f, if f has a singular point at x = c, then f has a local extreme point (i. e., max/min) at x = c. 2. For all functions f, if f has a local extreme point (i.e., max/min) at x = c and f is continuous at x = c, then x = c is a critical point of f 40 20 - 5 0 20 40 Figure 1: Question 6.3 (15 minutes) The graph of the DERIVATIVEy = f'(x) is shown in Figure 1. Assuming that y = f'(x) does not change its monotonicity and concavity outside of the region shown on Figure 1, determine the intervals where y = f(x) is concave up