For what value of x does the function f(x) = x - 3x attain the absolute maximum in the interval [-1,4]? %3D А. x = 0 B. x = 2 C. x = -1 D. x = 4

Q: The minimum value of the function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant x? + y² =…

A: To find the minimum value of the function f(x,y)=(x-1)2+(y-1)2 subject to constraint x2+y2=8. Let,…

Q: Find the interval on which the graph of f(x)=ln(x^2+1) is concave upward ?

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Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

Q: The graphs above are approximate graphs of f and f' for f(x) = x°(x – 12). So f is decreasing (and…

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Given function is  y=3-t-3,   -1, 5

Q: Find the consumer's surplus if the demand for an item is given by D(x) = 72- x, assuming supply and…

A: solve the following

Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3

A: f(x) is continuous at x = k if

Q: For æ = 4 the function f(x) = x? + bx +c has the minimum value of -9. Fine

A: The given function is f(x)=x2+bx+c has a minimum value = -9 at x = 4.

Q: ind the maximum and minimum values of the function f(x, y) = e"y subject to a + y = 54 laximum…

A:

Q: The function f whose tangent has slope x3. +2 for each value of x and whose graph passes through the…

A:

Q: 3. For which function is the average rate of change over the interval 1 < x < 5 greater than the…

A: To find- For which function is the average rate of change over the interval 1 &lt; x &lt; 5 greater…

Q: For function f(x,y) to have minimum value at (a,b) value is? 1) rt - s>0 and r0 and r>0 3) rt - s?0…

A: For a function fx,y to have minimum value at a,b, which of the given condition is true? 1)…

Q: (1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest…

A: The line whose equation is of the form y=mx is passes through the origin and slope of the line is m.

Q: 4. Find the absolute extrema for the function f(x)= on the interval -5 ≤x≤0.

A: To find the absolute extrema of the given function in the interval [-5,0].

Q: The function f is given by f(x)=9.x^2/3+3x-6 has a relative minimum at x=? A. -8 B.-1 C.-1/8 D.0

A:

Q: A textbook company estimates that the weekly marginal cost associated with producing x textbooks is…

A: topic - differential equations

Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Find the absolute extrema of h(x)=3x÷2 on {-2,3}.

A: H(x) is the straight line so absolute extrema will be at ends on domain

Q: Find the absolute extrema of the function on the closed interval.

A: Solution Given Find the derivative of the functionf'(x)=xx2+1To find the criticle Number derivative…

Q: Q6. The price received from sales in OMR per unit is given by p=x +x+1. i. the revenue function, ii.…

A: This question can be solved using the concept of marginal revenue.

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: 13. For the function f(x) = (x – 2)² + 4 where is the function: a. increasing? b. decreasing? c.…

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Q: On what interval(s) is the function f(x) = x* – 4.x³ both decreasing and - up? concave A

A:

Q: The function y = has a: a) local max of % b) absolute max of % c) local min of % d) absolute min of…

A: The given function is: y=1x2+4

Q: Find the absolute extreme values of the function on the interval. 3) f(x) = In (-x), -5 s x s -1

A:

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 16 x = 180 when p = $5…

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Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: The given equation is Ct=8e-0.4t-e-0.6t. Equate the derivative of C to zero as follows:…

Q: What is the closest value to the instantaneous function at x = 2? f(x), 2x-1 3x+1 O_1 49 O. 49 1 49

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Q: For what value of x does the function f(x) 4x attain the absolute minimum = in the interval [-3,5]?…

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Q: Find the values of a and b so that f will be differentiable at x = 3.

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Q: If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,…

A:

Q: At which value of x for the function whose graph is shown below differentiable? -4 VO 8 10 12 14…

A: From the given graph, we have to find the points at which the function is differentiable

Q: At what value of x is f(x) a minimum when f(x) = L* et*dt?

A:

Q: · Suppose that t hours after the injection of x milligrams of adrenalin the response is R units…

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Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

A:

Q: Find the absolute extreme values of the function on the interval. f(x)=ln(x+2)+1/x , 1 less than or…

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Q: Consider a situation where there are bears around your campus. Since bears harm our campus life, a…

A: Given: The student group decides to remove the bear in which the removal cost is given as,

Q: Find the value of constants c and d that make the function below continuous at x = 4. x2 5x x 4 d +…

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Q: It is given that at x = 1, the function x" - 62x? + ax + 9 attains its maximum value in the interval…

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Q: Locate the absolute extrema (maximum AND minimum): f(x) = 10x(2 - lnx) ,  on the interval [1,e^x]

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Q: For what value of x does the function f(x) 4x attain the absolute minimum in the interval [-3,5]? А.…

A:

Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: On the graph of f ( x ) = sec ( x ) and the interval ( -2π, 0 ], for what value(s) of x does f ( x )…

A: f(x) = 1 on, (-2π, 0] Implies, sec(x) = 1 on (-2π, 0] i.e. x = 0 on (-2π, 0] So, x = 0  The graph of…

Q: Please

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Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value(s) of x does the graph cross the…

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Let C be the concentration of the antibiotic in μg/mL t hours after the antibiotic is taken. Given…

Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: If 0 = KHLV-, where k is a constant, and there are possible errors of ±1 per cent in measuring H, L…

A: We will find out the required value.

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.