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- Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.For −10≤x≤14the function f is defined by f(x)=x^3(x+3)^4On which two intervals is the function increasing (enter intervals in ascending order)? x = to x = andx = to x = Find the interval on which the function is positive: x = to x= Where does the function achieve its minimum? x =
- For what value of x does the function f(x)=1/3x3-4 attain the absoulte maximum in tyhe interval [-5,3]?On the graph of f(x) = cotx and the interval [ − 2π, 0π ), for what value(s) of x does f(x) = 1?Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which consists of line segments and semicircles of radius 3 connecting the points (−8, 0), (−6, 6), (0, 6), (6, 6), (8, 0). What is the multipart formula for y = g(x) when -6 <= x <= 0 and when 0 <= x <= 6?
- For the function f(x) = 3x2 −x3 − 4 where −3 ≤ x ≤ 3, complete the following. 12. State the values of x for which f is concave up within the given interval. Use interval notation. 13. State the values of x for which f is concave down within the given interval. Use interval notation. 14. Evaluate f at its critical point(s). 15. Evaluate f at the endpoints of the given interval. 16. Identify the coordinates, in the form (x, y), of the local and absolute maximum and minimum of f in the interval [−3, 3]. Local Maximum: Local Minimum: Absolute Maximum: Absolute Minimum:On the graph of f(x)=cosx and the interval [2π,4π), for what value of x does f(x) achieve a maximum? Choose all answers that apply.The revenue from the sale of x mineral-based makeup sets is given by R(x)=42x−0.4x^2 dollars. The total cost is given by C(x)=0.1x^2−30x+2430 dollars, where 0≤x≤110. Determine the interval of sales for which the profit is increasing and the interval for which it is decreasing. Express your answer in open intervals.
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