(A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second derivative test to find the maxima and minima for f(x) = - 2x2 + 3x + 1. 3

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: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

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

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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: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

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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 numbers of the function f(x) = x6(x – 4)2. (b) What does the Second Derivative…

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Q: 4. Find the local maximum and minimum values of f, using both the First and the Second Derivative…

A: The given function is fx=x2x-1. Compute the critical points as follows.…

Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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

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Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

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Q: 2. a) Find and fully factorise the derivative of f(x) = (2x + 1)2 using expansion and the power…

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Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: 4. Find the critical points of the function. Then use the second derivative test to determine which…

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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: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

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: 4. Find the point on the graph of f(x) 5x2 + 20x – 3 where the tan gent line is horizontal. (a)…

A: We have to solve integration

Q: 3) Find the critical points of the function. Then use the Second Derivative Test to determine…

A: Given:- f(x, y) =4x-3x3-2xy2 To find:- Local maximum, minimum and saddle point

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: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

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: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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

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Q: 1. Sketch the graph of the function 4x f(x) = x E (-00, 00) 1+4x² Be sure to calculate the local…

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Q: Given the function f(x) = – x° – 6x2 + 5x + 12 , use either the First Derivative Test OR the %3D -…

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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: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 15 over the interval [1,3].

A: To find the extreme values of the given function f(x) = x2 - 3x + 15 over [1, 3]

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

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Q: Given the function g(x) = 4x° + 36x + 60x, find the first derivative, g' (x). %3D = (2),6 Notice…

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Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

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Q: (A) Find the absolute maxima and minima for x3 y = - x + 5 over 3 [-V2, v2]. (B) Use the second…

A: When on critical point f''<0 then that critical point give local maximum value of f(x)  When on…

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: Consider the function f(x) = 3x4 + 20x³ – 144x² + 54. (a) Find the critical numbers of f(x). (b) Use…

A: Given,   The function  fx = 3x4+20x3-144x2+54  We have to solve for part a, b and c.

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

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

A: See the attachment.

Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: 6. Find the values of x for which the line tangent to the graph of f (x) = 4x2 – 3x + 2 has a…

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Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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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: 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…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.