1 Consider the function U(x)=(x²-1) In(1-x²). (a) What is the domain of the function U(x) (i.e., where it is defined)? (b) Determine whether the function U(x) is odd, even, or neither. (c) Find the critical points of this function and determine its nature. (d) Plot function U(x) and show critical points.

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

Find (a) (f + g)(x), (b) (f – g)(x), (e) (f · g)(x), (4) (4) (x). What is the domain of (d)? 1) f(x) = 3x – 6, g(x) = 3 – x 2) f(x) =9(x) = x' +1 Evaluate the indicated function for f(x) = x² – 2 and g(x) = x – 1 algebraically. » )e - 2) 3) F – 9)(2) Find (a) (f • g)(x) and (b) (g • N(x) 5) f(x) = x* – 4, g(x) = Vx + 4 6) f(x) = x² + 9, g(x) = vF Use the graphs of f and g to evaluate the functions: 7)(a) (f – 9)(1) (b) (f - 9)(4) 8) (a) (f • g)(1) (b) (g • )(3) 8(x) y = f(x) y = g(x)

Match the function with its graph. (a) f(x) = x (c) f(x) = Vĩ (b) f(x) = x' (d) f(x) = |x| I II III IV

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f(x) = (x + 1)2 (x − 2) (a) Determine the x intercepts and y intercepts. (b) Determine the equations of any asymptotes. (c) Determine the first and second derivative of the function. (d) Complete a sign chart for f 0 (x) to determine the intervals where the function is increasing/decreasing. (e) Determine any relative extrema. (f) Complete a sign chart for f 00(x) to determine the intervals where the function is concave up/down. (g) Identify any points of inflection.(h) Complete a sketch of the function that supports all of the information above.

U.S. AIDS Deaths The function D defined by D(x) = 2375x² + 5134x + 5020 models AIDS deaths x years after 1984. Write a for- mula g(x) that computes AIDS deaths during year x, where x is the actual year.

In a chemical reaction, the reaction rate R is a function of the concentration x of the product of the reaction. For a certain second-order reaction between two substances, we have the formula below in function notation. R(x) = 0.01x2 - x + 19 The concentration x is measured in moles per cubic meter, and R is measured in moles/m3·s. (a) Calculate the value of R(18). Express to a maximum of two decimal places. _____moles/m3·s(b) Calculate the value of R(21). Express to a maximum of two decimal places. _____moles/m3·s(c) The reaction is said to be in equilibrium when the reaction rate equals zero. At what two concentrations is the reaction in equilibrium? Hint: Let R(x) = 0. Express answers to nearest whole units._____moles/m3 (smaller value)_____moles/m3 (larger value)

Consider the function: Answer f(x) = (3x² + 6)² Use the Second Derivative Test to classify the relative extrema, if the test applies. Otherwise, use the First Derivative Test. Keypad Keyboard Shortcuts Write all relative extrema as ordered pairs of the form (x, f(x)). (Note that you will be calculating the values of the relative extrema, as well as finding their locations.) Separate multiple answers with commas. Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. Relative Maxima: Relative Minima: O No Relative Maximal O No Relative Minimal

The price p​ (in dollars) and the demand x for a particular clock radio are related by the equation x=2000−20p.   ​(A) Express the price p in terms of the demand​ x, and find the domain of this function. ​(B) Find the revenue​ R(x) from the sale of x clock radios. What is the domain of​ R? ​(C) Find the marginal revenue at a production level of 1200 clock radios. ​(D) Interpret R′​(1600​)=−60.00.