can you please explain these questions.

1. Find the absolute maximum value and the absolute minimum value, if any, of the given function. x) =x3 + 3x2 - l on [-4,4] 2. Find the absolute maximum value and the absolute minimum value, if any, of the given function. x+5 xS x) = 011M991 3. A stone is thrown straight up from the roof of an SO- building. The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by 120) = 16:2 + 4n: + 50 What is the maximum height the stone reaches? 4. The management of Trappee and Sons, producers of the famous TexaPep hot sauce, estimate that their prot (in dollars) from the daily production and sale of x cases (each case consisting of 24 bottles) of the hot sauce is given by 90:) = - 0.000003x3 + 9x - 100 What is the largest possible prot Trappee can make in 1 day? 35 5. Find the derivative of the function by using the rules of differentiation. 3 2 x=- ft) x3 x10 6. Find the slope and the equation of the tangent line to the graph of the function f at the specied point. $0 = 5+ %; [g] 7. Find the third derivative of the function. Ax) = 2x- - 3x4 + 4x2 - 10x + 12 8. During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was A() = -0.00006/3 + 0.00468/4 - 0.1316+ 1.915#2 - 17.63# + 100 percent of the original amount. Compute A'(3), A"(3). Round your answer to the nearest thousandth. A'(3) = % per minute A"(3) = % per minute in the second power 9. Find the derivative of the function. Ax) = 219x10. Find the derivative of the function. Aw)= e+2 11. Find the derivative of the function. Ax) = 5x"In2x 12. A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is C(x) = 0.0002x - 0.08x-+ 120x + 5300 where x stands for the number of units produced Please give the answers to two decimal places. What is the actual cost incurred in manufacturing the 101st oven? What is the marginal cost when x = 100? S 413. Find the relative maxima and relative minima, if any, of the function. g(x) = 4+ 5 X Relative maximum: Relative minimum: 14. Find the relative maxima and relative minima, if any, of the function. A(x) = - 3x 4+ x2 Relative maximum: Relative minimum: UT