Given: f(x)= = x³ x²-3' with f'(x) = x4-9x² (x² - 3)² and f"(x) = 62³ +54x (x² − 3)³ Make a table that shows the intervals where f is increasing or decreasing, and where the graph of f is concave up or concave down. Specify in the table all relative minimum points, relative maximum points, and points of inflection of the graph of f. Sketch the graph of f. Reminder: Emphasize concavity in your graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymp- totes and label them with their equations.

Can the average rate of change of a function be constant?

Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative test. The first value will be the relative maximum and the second value will be the relative minimum.

Find the absolute maximum and minimum value of the function  f(x) = x / 49 + x^2

A company estimates that it will sell N(x) units of a product after spending Sx thousand on advertising, as given by N(x) = - 0.25x + 22x³ - 472.5x2 + 83,000, where 21 sxs45. When is the rate of change of sales increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate o change of sales? Graph N and N' on the same coordinate system. The rate of change of sales is increasing on (Type your answer in interval notation.) The rate of change of sales is decreasing on (Type your answer in interval notation.) The point of diminishing returns is thousand dollars. The maximum rate of change of sales is sales per thousand dollars. (Round to the nearest whole number as needed.) Graph N and N' on the same coordinate system. Choose the correct answer below. O A. В. с. D. 110000- 110000- 110000- 110000- N N' N' N' N' 0+ 16 0- 16 0+ 16 0+ 16 50 50 50 50

let'say. If 3(a) The cost of manufacturing motor cycles (per day) is related to number to number of motor cycles produced, per day. If the cost function (C) is related to the following equation as given, determine the optimum number of motor cycles that need to be produced, daily, corresponding to minimum cost. Note that X denotes total number of motor cycles manufactured per day. Total Cost (C) in SAR= (1/3)* x²- 200-X -50000*X.

Find & values of all points on the graph of + 3x² -11x +5 where the slope of tangent line is g=x² negative Total:/

Let f(x) = 5x and g(x) = ex + 7. Determine the x-coordinate where the graphs of the two functions intersect_ 0x = = = = O x = In(5) + 1 O x = -1 Ox=- 7 In(5) - 1 -1 5 + In(7) O x = In(5) - 1 O x =

Let f(x)=kx^-1+x^2 For what values of k, function f(x) has a relative minimum but not a relative maximum?

Determine the slope of the secant line for the following function that passes through the given points. f(x)= 2x^2 +1, P(1,3), Q(3,19)