please do the following problems and show the work

The First Derivative Test 92. Draw a picture of a continuous function y 2 x} that increases. decreases. and in creases again. Use your drawing to do the following. {a} Mark a point a on the raxis where f'fo} :- i]. {b} Mark a point in on the raxis where ffh} 4-: 4]. {c} Mark a point e on the raxis where either f'{c} = I] or the tangent line does not exist. 93. {a} 1What can you say abou the original graph 1; 2 HI] at the point a where f'oj 3: I]? {b} 1What can you say abou the original graph 3,; 2 HI} at the point in where f'bj c: I]? [c] 1What can you say about the original graph 3.; = HI} at the point c? {d} Does your graph have any local maximums? 'Where are they? lie} Does your graph have any local minimums? 1Where are they? 94. Suppose I is a function. {a} Is it possible for a continuous function y 2 x} to have a local maximum at a point (c, I: f [12]], even though the graph does not have a tangent line there? If this is possible, draw an example. {b} Suppose that a continuous function f has a local maximum at I = c and that the tangent line to the graph exists at that point. 'What can you say about the tangent line? 1What does that tell you about the 1.ralue of the derivative fIEc}? {c} Explain your results. What have you discovered? {d} On the other hand. suppose you know that the graph of y = 9(1) has an horizontal tangent line at .T = c. 'Would that be enough for you to conclude that g has a local max}:E min at .1: = c? Explain