Thank you!

1. Consider the function f (x) = x + sin(x) , restricted to the domain [-2, 4). Your goal in this problem is to use your calculus skills to confirm what you see in the graph of this function. So, you may consult the graph on desmos to guide you, but your submitted work should include enough details and explanations to convince a classmate reading along that everything you found is correct. 1. Determine when the function is increasing and when it is decreasing. 2. Determine any critical points, and use the First Derivative Test to classify them. If that test does not apply to a certain point, or doesn't guarantee anything meaningful, explain why that is the case. 3. Determine when the function is concave up, when it is concave down, and where any inflection points occur. 4. Use the Second Derivative Test to classify any critical points. If that test does not apply to a certain point, or doesn't guarantee anything meaningful, explain why that is the case. 5. What does the Extreme Value Theorem & tell us about this scenario? Does it guarantee anything? If not, why? And if so, explain what it guarantees and then find it/them. 2. Repeat the previous exercise but with the function g (a) = x . e-x/4 on the domain [1, 12] instead. 3. Repeat the previous exercise but with the function h(a) = (a + 3) (x - 4) 5 on the domain [0, oo) instead