(A) Find the absolute maxima and minima for y 4x +1 over 3 - [-V5, V5]. (B) Use the second derivative test to find the maxima and minima for f(x) 3 3x 10x + 5. 2 -

Q: Let f(x) = x² – 8x – 14 Use the second derivative test to find any local maxima and minima. First,…

A: for critical value put first derivative zero if second derivative positive minima and if negative…

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3].

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Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: Find the local maximum and local minimum values of f using both the first and Second derivative…

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

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Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

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Q: 11.  Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to…

A: Given information:The given function is shown below:

Q: Find an equation of the curve whose tangent line has a slope of f'(x) = 4x 14/15 given that the…

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Q: (a): Find the critical points of the function f(x) 6x2 12x. (b): Apply Rolle's theorem for the…

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Q: 5. Use the given derivative to find all critical points of f and at each critical point determine…

A: Given that, f'(x)=4x3-9x

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

Q: 12. Consider the function f(x) = 2x3 - 9x2 + 12x – 3. %3D (a) Find the critical values of f, that…

A: f(x) = 2x3 - 9x2 + 12x - 3 f'(x) = 6x2 - 18x + 12    [As derivative of xn = nxn-1]

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

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Q: Consider the function f(x) = 52° + 12x – 7. %3D (a) Find the derivative f'(x) and hence the critical…

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Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: Given the function f(x)=x4-6x2-60x2+134x+30 The value x=1 satisfies the equation f'(x)=0 (that is,…

A: The function f(x) is maximum when f''(x)<0 at x=a The function f(x) is minimum when f''(x)>0…

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: 12 11. Find the critical points of f(x) 4x? ). Then use the Second Derivative Test to determine if…

A: Here, we need to find the critical points of f(x)=x127x3-4x2. Now, f'(x)=6x2x-10xx and…

Q: 9. Given the function f (x) = 3x -4x2 + 2, use the first and second derivative tests to find: a) the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270. f(x) has one local minimum…

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Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: b. Use the Second Derivative Test to find all local minima and local maxima for g(x).

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Q: Find any critical numbers and apply the First Derivative Test to identify any relative extrema. а)…

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Q: Find a root of an equation f (x) = 4.15x3-2x+5.15 using Incremental search method at a step- size…

A: Given: f(x)=4.15x3-2x+5.15, a=-2 and b=-1 To find: Root of a given equation by Incremental search…

Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

A: Given,  fx = x2-4x+9    We have to find the absolute extremum values in the interval 1, 4

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 10 over the interval [1, 3].

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Q: Consider the function y = -x3 + 3x² – 2. a) Find the critical points. b) Use the 2nd Derivative Test…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: 3) Find the absolute maximum and minimum values of the functior F(x)= Vx on the interval -1sx< 8.

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

Q: Find the critical points of f(x)=3x^4 -4x^3 +5 and use the first derivative test to determine local…

A: Given,          fx=3x4-4x3+5

Q: Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1)…

A: To find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of…

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…

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.