In this homework we will analyze the function f (x) = en/2 _ garccot(x2-1) Note: arccot (x2 - 1) is the power to which e is being raised. We will consider [0, 7] as the domain on which cot(x) is invertible. We want to use our calculus skills to create a decent graph of this complicated function. This homework will walk you through collecting relevant data. Then you'll use the data to draw your graph.a) (4 points) We will need the first two derivatives of our function. On the lines below, write expressions for f'(x) and f"(x). (Note: No work needs to be shown for this part. At this point in our class, you may want to explore calculators such as WolframAlpha.com and Symbolab.com, which can find derivatives automatically.) F(x) = F(x) = b) (4 points) Build a sign chart for f/(x). [Hint: x* 2x% + 2 = 0 for all x] ) (2 points) In your own words, explain what the sign of f'(x) tells us about the graph of f(x). This answer does not need to be very long. \fe) (2 points) In your own words, explain what the sign of f\"(x) tell us about the graph of f(x). This answer does not need to be very long