The average pollen count in a certain city on day x of the pollen season is P(x) = 12x - 0.2x2 (for 0 < x < 60). On which day is the pollen count highest? X =

Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

Q: Find the intervals in which the function f(x)=3x -18x² +7 is increasing/decreasing. Also find the…

A: For function f(x) you can find the intervals in which f(x) increases by solving f'(x) &gt; 0. For…

Q: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: The total-revenue and total-cost funtions for producing x clocks are R(x)=500x-0.01x2 and…

A: The total-revenue and total-cost functions for producing x clocks are The profit function is

Q: For finding the root of the function: f(x) = 3x – x² Do 2 steps of the bracketing method, given the…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: In the function:  f(x)= (4x^2)/((x^2)+4)  What are the critical numbers of the function?  Where is…

A: Given function

Q: maximum revenue for the revenue function  R(x) = 372x − 0.7x2.  (Round your answer to the nearest…

A: Please refer to the image below

Q: 3. Find the absolute maximum and absolute minimum values of f(x) = 2x´ - 4ln(x) on the | interval […

A:

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Given equation is: y = -3x - 16

Q: At a certain vineyard it is found that each grape vine produces about 10 lbs of grapes in a season…

A: To find the number of vines that should be planted to maximize grape production.

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

A:

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: The critical points of a function are points where derivative equals zero or derivative does not…

Q: A piece of cardboard measuring 12 inches by 13 inches is formed into an open-top box by cutting…

A:

Q: A producer of door frame chin-up bars has determined that the revenue from the production and sale…

A: A function is said to be increasing if f'x&gt;0. A function is said to be decreasing if f'x&lt;0.…

Q: Find the absolute maximum and minimum values of ƒ(x) = x2 on[-2, 1].

A: Given,  fx=x2 on −2,1

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: The critical points of the function are the points where the function is defined but its first…

Q: An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: As we are making a box, its height must be greater than 0. So we have x&gt;0. As the width of the…

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We know that Critical points are points where the function is defined and its derivative is zero or…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Given function is, fx=x4+16x3+64x2+4.   a. To find the critical numbers.   First, differentiate the…

Q: Find the x-values corresponding to all critical points of the function f(x)=1/5x5-a4x,  where a is…

A: We have to find critical points

Q: 3) Given f(x) =-2x -2x-2, find the absolute maximum value over the interval [0,6].

A: We have to slove the above question and find absolutely maximum value

Q: At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season…

A:

Q: Find the critical numbers of the function.…

A: Critical numbers : f(x)=4x2-6x The derivative of the function is f'(x)

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Solution:Given        f(x)=xe-3xTo find:(a)Critical Point(b)the open interval where the function is…

Q: Find the critical number and the open intervals on which the function y=x^3-3x+2 in increasing or…

A: y = x3 - 3x + 2  dy/dx = 3x2 - 3

Q: The profit function of a company is P(x) = x² – 400x + 40000, then the break-even poi is %3D

A: The break-even point point occurs when the total revenue is equal to the cost. At that point, the…

Q: of all real numbers x such that -3 < x < 5. (a) For what values of x does f have a relative maximum?…

A: at x=-3 and x=5 f is relative maximum

Q: 1. Find all local max/local min values of f(r) = x² – 6x – 1

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: 2. Use the Closed Interval Method to find the absolute/relative extreme values of the function f (x)…

A: Solve the following

Q: 3. Find the intervals of increasing/decreasing of the function -4x' +16x² – 20.Also find the local…

A:

Q: Find the critical numbers of the function. (Er g(x) = x6 – 3x4

A: To find the critical numbers we first find g'(x) using the power rule

Q: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a…

A: Given model of the equation is simplified by expanding the brackets:

Q: g(x) = x' + 3 x² – 24 x

A: The point x=k is said to be the critical point of the function f(x) if Case 1 : f(k) exists and…

Q: The function f (x) 2x3 – 39x + 216x + 2 has derivative f'(x) = 6x? 78x + 216. f(x) has one local…

A: Function will have a local minimum at a point where the value of the derivative of the function will…

Q: Absolute maximum value on (0, ) for 8. 12 f(x) = 20 – 3x -

A:

Q: Find all critical points of f(x) = 2x³ + 2x-. (Use symbolic notation and fractions where needed.…

A: First, we find f'(x) using the power rule

Q: 2. Find the absolute maximum and absolute minimum values of function on the given interval. f(x) = 5…

A: Given:Given that function f(x)=5+54x-2x3The given interval is [0,4]To find:we have to…

Q: Find the absolute maximum and minimum of

A:

Q: As dry air moves upward, it expands and, in so doing, cools at a rate of about 1°C for each…

A: Answer for the question will Start by writing the expression describing the value of temperature…

Q: or equal to 0). Find the minimum possible value of X346.

A: here given mean of 345 quantities is 5.9

Q: x+2 for 4. Graph. f(x) ={-V4 – x² for -2 sxs2 (-x(x-3) for x 2 f(x)t

A: Consider the function  f(x)=12x+2                 for x&lt;2−4−x2            for−2≤x≤2−xx−3…

Q: 4. Find the absolute extrema (abs. max and min) of f (x) = x2 - 8x - 1 on the interval [1, 10].

A:

Q: Find the absolute maximum and minimum values of f(x) = 2x³ – 36x2 + 120x -8 on the interval [0, 12]…

A: