By using Mean Value Theorem, verify the following options to the function f(x)= 1 on [1,4]. %3D Here f(1)= 1 and f(4)=0.25 Choose... c= -2E(1,4) Choose... c=2E(1,4) Choose...

Q: From the following data compute the value of harmonic mean: Class interval 10-20 20-30 30-40 40-50…

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Q: calculate the average over the given interval. f (s) = s −2, [2, 5]

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Q: Which one of the following functions fails to satisfy the hypotheses of the Mean Value Theorem on…

A: Mean value theorem states that "f be a function which is continuous on a, b and differentiable on a,…

Q: From the following data compute the value of harmonic mean: Class interval 10-20 20-30 30-40 40-50…

A: Given data is Class Interval Frequency 10 - 20 4 20 - 30 6 30 - 40 10 40 - 50 7 50 - 60…

Q: Given that , find the value for c such that f(c) equals the average value of f(x) = x2 over [0, 3].

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Q: let x has the p.d.f f(x) = {3xe* 3xe-V3x 0 < x < c0 0.W By m.g.f find the mean and variance of the…

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Q: Q - 16 From the following data compute Bowley's coefficient of skewness and interpret your result.…

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Q: Let X b(16, find E(4-3x) and distribution function.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Give the value of c in the interval [0,2] that satisfies the conclusion of the mean value theorem…

A: We have been given a function g(x) = 4sqrt(x)-3 and we need to find the value of c on the interval…

Q: Suppose that E (X1) = E(X2) = E(X3) = µ, Var(X,) = 5, Var(X2) = 8, and Var(X3) = 13. Find c so that…

A: Introduction: An estimator for the population mean, μ is said to be unbiased, if the expected value…

Q: Suppose that h(x) is the hazard function of X, and h(x)=?λ for all x. (a) Calculate the survival…

A: Given: H(x) is the hazard function of X and h(x)=€,a constant

Q: Let f(x) = x/r +8. Answer the following questions. 1. Find the average slope of the function f on…

A: Given function is, fx=xx+8

Q: If h (x) = 4x² – 15x – 9 on the interval [-1, 3]: Apply the mean value theorem to find the value of…

A: We can use the mean value theorem in order to solve the given problem.

Q: Given f (x) = 4x²-3x + 2. The slope of the normal line to this curve at the point (1,3) is O-5 5…

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Q: The following data is given: pO = 1500 T0 = 1/3 T 1= 2/3 Σ 1250 u1 = 5200 Using linear…

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Q: Given that, S(C) = 2sin( 3t) %3D Find the mean value of f(t) in the interval 0 <t < 5, correct to…

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Q: Let f(x) = xVx + 5. Answer the following questions. 1. Find the average slope of the function f on…

A: Given, f(x)=xx+5

Q: Consider the data below in the range 0.4 s xs 1.2 0.4 5.1600 1.4 3.3886 2.2 5.7491 0.6 3.6933 1.6…

A: given data in the range 0.4≤x≤1.2 claim- calculate P30.9 using last four points. given last four…

Q: From the table (data set) given below, calculate f(0,2) by Lagrange Interpolation method. - 0,2 0,1…

A: The solution is given as

Q: Let t represent the total number of hours that a truck driver spends during a year driving on a…

A: Probability of at least one accident = p(t) Probability of no accident = 1 - p(t)

Q: Let X - T(25). Find P30(X) (30th percentile of X)

A: Solution: From the given information, X follows T distribution with degrees of freedom 25.

Q: For a​ t-curve with df=9​, use a​ t-distribution table to find the​ t-value t0.025.…

A: From the provided information, Degree of freedom (df) = 9 The level of significance (α) = 0.025

Q: The lengths of the segments are defined by the functions s1(x) = 9x - 1, s2(x) = 2x + 3, s3(x) = 4x…

A: The lengths of line segments are s1 (x)=9x-1 s2 (x)=2x+3 s3 (x)=4x-7 s4 (x)=x-3

Q: For the following discrete variable with probability f(x) X 1 2 3 4 f(x) 0.2 0.15 2с 0.05 0.15…

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Q: 9. For the following data, test the hypothesis that a relationship exists between X and Y. .30, N =…

A: rxy = 0.30, N =61

Q: Let x1, X . ,~ Bin( n,p) and p = . Find 1) A constant c such that E[c p ( 1 – p) ]= p(1- p). 2) Find…

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Q: From the following data compute the value of harmonic mean: Class interval 10-20 20-30 30-40 40-50…

A: Given: Class interval 10-20 20-30 30-40 40-50 50-60 Frequency 4 6 10 7 3

Q: Consider the following table of data: 0.4 0.6 0.8 1.0 f(x) 0.9798652 0.9177710 0.808038 0.6386093…

A: The given question is:

Q: BE Drfferentiatethe above relation 20ith respect to p

A: We will apply the concept of differentiation of product of two function

Q: Given the following data, find the best fitting function, then Provide the value of a in the model…

A: By method of least squares, form the normal equations by multiplying the model by ∑i=14xi and…

Q: Calculate Karl Pearson's Co-efficient of skewness from the following data Number of Students Marks…

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Q: ch of the fOllowing scales would be best f O black, non-black O white, black, Hispanic, Asian, other…

A: Research as a scientific and systematic approach for pertinent information on a specific domain…

Q: Give the value of c in the interval [-1, 2] that satisfies the conclusion of the mean value theorem…

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Q: Find the average value of the following function: p(x) = 6x2 + 5x + 3 on the interval 1 < x < 3.

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Q: Find the value of c which satisfies the Mean Value Theorem with the given / (x) =e", [0, 1]. A Inx…

A: Given, f(x)= ex [0,1] b=1 a=0

Q: From the following data compute the value of Yule's Coefficient of Association and find out its…

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Q: A manufacturer makes thousands of ballpoint pens per day, and estimates that 3% are defective and…

A: Given : A manufacturer makes thousands of ballpoint pens per day, and estimates that 3% are…

Q: In a pediatric clinic, a study is carried out to see how effective drug X is in reducing…

A: before after  d(after- before)   102.4 99.6 -2.8   103.2 100.1 -3.1   101.9 100.2 -1.7   103…

Q: he price of a memory card depends on its storage capacity--the larger the disk the more expensive it…

A: Here we have,  The prices for several popular memory card sizes are displayed in the table below.…

Q: If W denotes the weight (in pounds) of an individual and t denotes time (in weeks), then dW/dt is…

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Q: From the following data calculate first four moments and also find the value of r, Monthly profits…

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Q: Let f(x) = rVx+ 4. Answer the following questions. 1. Find the average slope of the function f on…

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Q: The joint probablity function for X and Yis gven below. E(2X + 3Y) is __ 1_. 0.35 0.25 023 0.17…

A: We have given that the joint distribution function of X and Y in tabulation form.

Q: Obtain the mean value A(f) of the given function in the given interval: S (x) = Vx , [0,9]

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Q: Calculate Semi-Inter-Quartile Range and its Co-efficient of Q.D. from the following Vata : Marks…

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Q: Q2 find the mean and variance of the following distribution .f(x)= 6x(1-x) , 0<x<1 Also find P (µ ·…

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Q: From the following data of the daily wage of 500 workers of a factory find the number of workers :…

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Q: Suppose f"(x) = N¿(h) + a,h + azh² + azh³ + -· The value of N½(h) using Richardson's extrapolation…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Which of the following correctly relates the average cost function Cave(x) to the marginal average…

A: Average cost is the total cost is divided by the number of items. Marginal cost is the amount of…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.