Let f(x) 2x2 - 8x + 4. (a) Find the critical point c of ƒ and compute f(c). (Give your answers as whole numbers.) C = f(c) = (b) Find the extreme values of f on [0, 5]. (Give your answers as whole numbers.) Мaximum: Minimum: (c) Find the extreme values of ƒ on [-4, 1]. (Give your answers as whole numbers.) Мaximum: Minimum:

Q: Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum…

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the…

A:

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A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find…

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A:

Q: Q2 (a) Let f (x) = x* - 4x³ + 10 (i) Find all critical points of f(x). Determine whether the…

A: For, critical points we take f'(x) =0 For, inflection points we take f''(x) =0

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A:

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Q: If f(x) = x – kx-1 has a relative maximum at x = -2, then the value of k is %3D

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: Given that

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A:

Q: f(x) = x2 -x-7 is The relative maximum value of and its relative minimum value is

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Q: Find the minimum value of f (x) = 7x² – 2x + 4 on the interval (0, 1].

A:

Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

A:

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A: For the function f(x)=x4-4x3+2, to identify the critical points, we will use second order derivative…

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A: we have to find value of a such that x=4 is a critical point. now,

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A:

Q: Q2// Find the optimal point from th nathematical model (by Big-M methods) xZ-150 x+110x)+280 x; x3…

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Q: The function F(x) = 2x^3 + 3x^2 has a relative minimum point at x =

A: We will solve the problem

Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

A:

Q: g(x) = V4– x²

A:

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A: Given,  fx=x2 on −2,1

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A: Solution: Given: f(x)=8x3+4x2-12x+10

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A: Solve the following

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A: Check the function has absolute minimum value.

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A: For finding critical points  Y' = 0 For maxima and minimum values find  Y"(x1) and Y"(x2)

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A:

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A: Answer

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A:

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A: We have to find

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A: Please refer the attached image for complete solution.

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A: Use derivative

Q: 25 f(x)=x²-3x x³ + 20x + 1; 1 = (-3,2)

A: As per the company's guidelines , we are supposed to answer only first question. Kindly re

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A:

Q: Find and classify the critical points off (x) = 6x°(5 – x)° as local maxima and minima.

A: Given that f(x)=6x55-x6 First let's find the extreme points, f'c=0 Take the derivative for f,…

Q: ¥ 5) Find all the critical points of f(x)= = = 2 and determine if they are a relative maximum,…

A:

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A: here, objective is to find  the critical points of the function f(x)=1/x on [1,8)

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A: Find f'(x) using exponent rule.

Q: Find the critical numbers and the local maximum and minimum values of the function f(x) = x* - 2x²…

A: Given :                   f(x) = x4 - 2x2 + 3

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Q: Find the minimum and maximum of x3+3x². on the interval [0, 3].

A:

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Q: Find the critical point of f(x) = -x² + 2x + 7 and determine if the function is increasing or…

A: For Critical points we will put f'(x)=0     And for determining  whether fxn is increasing or…

Q: y = x* – 4x +1

A:

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.