The function f(x) = 2x³ – 27x² + 108x + 6 has one local minimum and one local maximum. This function has a local minimum at a = vith function value and a local maximum at r = vith function value

Q: Does ƒ(x) = (7 + x)(11 - 3x) 1>3 have an absolute minimum value or an absolute maximum?

A: Here we have,  f(x)=(7+x)(11-3x)13 differentiate with respect to x

Q: What is the maximum point on the curve = 2 + 12? − x3

A: Maxima minima problem

Q: The function f(x) = 7x + 2x¯1 has one local minimum and one local maximum. This function has a local…

A: Consider the given function. f(x)=7x+2x-1                                       (1) Find the…

Q: The function f(x) = 2x²-3x+ k has a minimum -Find the value of k. 8. value of-

A: The function fx=2x2-3x+k has a minimum value 78. We have to find the value of k.

Q: The critical points of the function f(x)= 3x² -36x+1 are

A: To find critical point lets take first derivative of f(x)  and put f'(x) =0

Q: f (x)= xª + 4x³ – 4x 3 1

A:

Q: Find the absolute maximum value of g(x) -2x2 + x – 1 over [–3,5].

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the absolute maximum value of g(x)= 2x2 −2x−2 over [0,6].

A: We have to find absolute maximum value of f(x) in given interval.F(x) is given as:

Q: Find the absolute maximum/minimum of function f(x) = x3 - 16x + 1 %3D

A: fx=23x3-16x+1 to find the critical points take derivative=0 ddx23x3-16x+1=0 ddx2x33-ddx16x+ddx1=0…

Q: Find the maximum value of f(x) = - + 6

A: The maximum value of the function is the topmost point in the curves of the function. For a…

Q: Find the minimum value of the function. f(x) = -2 - 2x + x2

A:

Q: The function f(x) = 2x°- 36x+210x + 4 has one local minimum and one local maximum. Use a graph of…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 – 9x² –…

A:

Q: The graph of function f(x) = x³ 6x2 + 9x + 1 is concave upward on (-∞, 2) (-0, 0) (2, оо) о (-2, 2)

A: f is concave up when f''(x) is greater than 0

Q: The function f(x) = 2a* - 39x2 + 240x + 10 has derivative f'(x) = 6x² – 78x + 240. f(x) has one…

A:

Q: Find the minimum of f(x) = 3 + 6*x + 5*x2 +3*x3 + 4*x4 in the range of [-2, 1]

A: the given function is f(x)=3+6x+5x2+3x3+4x4 find the derivative  f'(x)=6+10x+9x2+16x3 find the…

Q: The function f(x) = 2x3 + 39x? 216x + 10 has one local minimum and one local maximum. - - This…

A: we will find the local maximum and local minimum.

Q: Find the absolute maximum and minimum values of f (x) = x³–6x²+5 on the interval [-3,5]. %3D

A: we find the absolute minimum and maximum value at the critical points and end point on the interval

Q: maximum number of turning points possible for the function f(x) = 9x* + 2a³ – 6x – 5, is

A:

Q: Find all values of x, if any, where the function f(x) = x5 - 5x3 - 20x - 2 has local maximum and…

A:

Q: The function f(x) = 7x + 8x 1 has one local minimum and one local maximum. This function has a local…

A:

Q: Find the absolute maximum and absolute minimum values of the function f(x) = -x3 + 12x + 6, over the…

A:

Q: The function f(x): – 2x3 + 30x² – 54x + 7 has one local min - This function has a local minimum at x…

A: Here we have to find the local minima and maxima of the function.  The given function is…

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

A: Given revenue function

Q: . Find the local and absolute minima and maxima for the function over (-∞, ∞). 3 y = x³ (1-x)6

A: Given, y=x31-x6

Q: Find the absolute maximum and minimum of ƒ(x) = 2x - 3x2/3 (a) on the interval [-1, 0.5]; (b) on the…

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: f (x) = x²-4x + 3, determine x such that f (x)> 3. what is the maximum value ?And the minimum value…

A: Given query is to find the values of x such that f(x) > 3.

Q: Find the absolute maximum/minimum of function f(x) = 4x3 - x2 - 2x %3D for interval of [0, 1]

A: The absolute maximum of a function in interval a,b is the maximum function value over this interval.…

Q: Consider the function f(x) = 2x° + 9x² – 108x +1 with - 6 <x < 4 | This function has an absolute…

A: Given, f(x) = 2x3 + 9x2 - 108x + 1  Plot the function on the interval -6&lt;= x &lt;= 4. For solving…

Q: Find the absolute maximum or minimum if it exists. 3. f(x) = 2x2 + 3x – 2 4. f(x) = 1 – x – x2

A:

Q: Find the absolute minimum of the function f(x) = x²³ - 3x² on the interval - 1 ≤ x ≤ 3. -4 3

A:

Q: Find the absolute maximum and absolute minimum of f(x) =2x3-3x2-36x+2 on the interval [0,5]

A:

Q: The weekly revenue (in dollars) earned from selling x porcelain vases is given by the function R(x)=…

A:

Q: Find the absolute maximum & miniumum of the function f(x) = x^4 − 8x^2 on the interval −1 ≤ x ≤ 3.

A:

Q: Find the absolute maximum of f(x) = x3 −6x2 + 12x + 3 on [0,3]

A:

Q: Find the absolute minimum and maximum of f(x) = 2x3 - 3x2 - 36x + 2 on [0,5]

A:

Q: . Find the absolute maximum and minimum values of f(x) = 2x3 − 21x2-21X 2+ 60x + 1 on the closed…

A: We have f(x) = 2x3 - 21x2 + 60x + 1 We find its derivative w.r.t. "x", f'(x) = 6x2 - 42x +60 To find…

Q: The function f(x) = 2x° 33x + 108x + 2 has one local minimum and one local maximum. This function…

A: first we calculate first derivative and second derivative.

Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

A:

Q: The absolute maximum value of the function y = 4x5 - 10x2 – 8 on the interval [-2, 2] is

A: Given: y = 4x5 - 10x2 – 8                                                     intervals [-2, 2]  to…

Q: The function f(x) = 2x³ − 33x² + 60x + 8 has derivative f'(x) = 6x² f(x) has one local minimum and…

A: Explanation of the answer is as follows

Q: 2. Find the local and the absolute maximum and the minimum values Ax) = x4 – 8x3 + 6x² + 40x + 3 of…

A:

Q: 3x2 If (x) = x² + 1

A:

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: The function f() = 2x - 33x2 + 168x +11 has derivative f'(x) = 6x – 66x + 168. f(x) has one local…

A:

Q: f = 2x – 3x²/3 on [-1,3].

A:

Q: Find the mascimum or minimum value of the function. F(x) = 2x² + 8x - 1

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.