Suppose that c = 3 is a critical number for a function f. Determine if f (c) is a local maximum, local minimum or neither if f' (x) =a 19 z + 30. a) O Local Minimum b) O Local Maximum c) O Neither

Q: 4. Use the Golden Search method to find the minimum of f(x) x2 -2sinx with interval from 10 X1 = 0…

A: clc; clear all; close all; fun = @(x) x.^2/10 - 2*sin(x); % defining function f(x) as inline xL = 0;…

Q: Find the critical numbers of the function f(x)=−6x5−15x4+10x3+2 and classify them using a graph.…

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Q: Suppose that f is defined everywhere and 1 are the only critical numbers for f. If f"(x) = 2x + 1,…

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Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

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Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2&gt;0 and r&gt;0 then minima will…

Q: Find thecritical points of the . function f(xy) and indicate with evidence whether they are local…

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Q: If f, (a,b) = f, (a,b) = 0, does it follow that f has a local maximum or local minimum at (a,b)?…

A: Given, fx(a,b)=fy(a,b)=0

Q: Find all critical numbers and use the First Derivative Test to classify each as a local maximum,…

A: To find the critical point and local maximum/minimum if possible

Q: Prove that if f(x)>0 and f′(x) exists for all x in the interval [a,b] then the square root  of f(x)…

A: Given: Prove that if f(x)&gt;0 and f′(x) exists for all x in the interval [a,b] then the square root…

Q: Lets find out all critical points of the function f(x, y) = xy +(2/x)+(4/y) and classify local max,…

A: Differentiate partially and equate it to zero to find the critical point, fx=0y-2x2=0y=2x2…

Q: Consider function f(x)= 2x -21x²+ 72X t 3. Determine 'which of the following at x=4 A. Not a…

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Q: Sketch the graph of a function f that has a local minimum value ata point c where f′(c) is…

A: Let the function is, fx=x Then, f0=0    and    fx≥0    for    every  x. This means that the function…

Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: :(- 2,2]– R, F(x) = L(-3(² + 1) dt

A: Given data :  F(x)=∫-2x2(t-3)(t2+1)dt

Q: Use the extreme value theorom (if applicable) to determine the absolute maximum minimum value of the…

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Q: show steps please

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Q: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.…

A: Sketch the graph of a function that is continuous defined on the interval [1,5] having the following…

Q: Decide if the given value of x is a critical number for f, and if so, decide whether the point for x…

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Q: Find the critical numbers for h(x)=x^2-x^4. Show all work.

A: The objective of the question is determine all the critical point of the given function.

Q: Show that 5 is a critical number of the function g(x)  = 2+ (x -5)3but  g does not have a local…

A: Critical number of a function is the value of x for which its first derivative is zero. So…

Q: 3. Let f(x) = 2x In(x). 3.1. Determine all the critical numbers to f(x). 3.2. For each critical…

A: 3.1. The given data is: fx=2 x lnx To determine all the critical numbers to f(x).

Q: Consider the graph of f(x) below: ... 2- -2 3 4 5 6 --1- -2 Which of the following statements is…

A: Solution )a) at x=6 relative minimum occur hence statement a is false  b) at x=2 absolute and…

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² | × [} then

A: 9

Q: Find and classify all critical points of the function 3 f(x, y) = x³ + 2y - In(x³y³) Item 5.pdf

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Q: If f has critical number at x=2, then f(2) is extreme value True O False

A: Explanation of the answer is as follows

Q: If f is continous on[0,1] then f has an absolute maximum on (0,1)   True or false?

A: We will do it by a counter example.

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

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Q: Determine the critical point and find for the maximum and minimum values at closed interval for the…

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Q: . Find the maximum value of f(x) = In(x – In x) on the interval -sxs. Show all steps .

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Q: Suppose that f is defined everywhere and x = 2 and x = -1 are the only critical numbers for f. If f"…

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Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

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Q: What is the absoluite extrema of the function h in interval [0, π]. Calculate and state the…

A: Exponential and sin, cos are always continuous

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Find all critical numbers of f (x) =4x³+3x²– 18x – 2 @ -- (A B -1 D) 1

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Q: The function f(x) = 10x – In(8x + 13) has a single critical number at x = A. Find this critical…

A: For critical number, f'(x)=0

Q: construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined.…

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Q: The set of critical numbers of f(x) =x³ - -x²+1 , are 2 A O {0,3} {-/3,/3} .BO .CO {3,3-} .DO {0.1}

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Q: 12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if…

A: We have to find critical points and state whether they are maximum or minimum using second…

Q: Let f(θ)=cos2(θ)−2sin(θ). Find the intervals where f is increasing and the intervals where f is…

A: fθ=cos2θ-2sinθf'θ=-2cosθ. sinθ-2cosθ=0⇒cosθ1+sinθ=0cosθ=0 , sinθ=-1θ=π2,3π2θ=3π2

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].

A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…

Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined.…

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Q: Apply golden section search in the interval [-1, 0] to locate the minimum of the function f(x) = x²…

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Q: If f is defined on [a, b], then f can't have a critical point at x = a. Select one: True False

A: We have to find out that Given statement is  True or false.

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: What are the absolute maximums and minimums of z(x) over its domain?

A: Given To find what are the absolute maximums and minimums of z(x) over its domain.

Q: Find and classify all critical points of the function f(x, y) = x + 2y - ln(x4y8) Item 5.pdf

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Q: ve an example of a function f where it does not have a global maximum on a closed interval [a, b].…

A: Global maxima of the function

Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…