A point on a curve is said to be an extremum if it is a local minimum or a lo maximum. The number of distinct extrema for the curve 3x- 16x + 4x2 +37 is | (a) 0 (b) 1 (c) 2 (d) 3

Q: Find the local minimum and maximum of y= x2/ 3 + x2

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Q: Compute the abscissa of the minimum point of the curve  y = x3 - 12x -9.

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Q: Does ƒ(x) = (7 + x)(11 - 3x) 1>3 have an absolute minimum value or an absolute maximum?

A: Here we have,  f(x)=(7+x)(11-3x)13 differentiate with respect to x

Q: 2. Find the critical points and determine whether they are a maximum, minimum or neither. y = a° –…

A: In the question we have to find the critical point also max. and min. points.

Q: Two nonnegative numbers whose product is 25a² (where a 0) and whose sum is a minimum, are

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Q: If  f has a local minimum value at , show that the function g(x)  =-f(x)has a local maximum value at…

A: Let  g(x)=-f(x) g'(x)=-f'(x) If f(x) is increasing in interval (a,b) , then  That is if f(x) is…

Q: Find the local maximum and local minimum in (x,y) notation for the following: y=(2x2-7x)/(2x+5)

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Q: Find global maximum and global minimum of æ3 – 9x? – 48x + 52 on the interval [-5, 12]

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Q: Provide an appropriate response. Given that x > 0, find the maximum value, if any, of x-x".

A: Given that x>0. We have to find the maximum value of  x1x5.

Q: Find the minimum value of x²+y² + z²,

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Q: Show that the interval [0,1) does not have a maximum element; that is, there is no largest number…

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Q: What is the absolute minimum of p(x)=2x2 −x−2 over [−2,6]?

A: Obtain the derivative of the function as follows.

Q: Given ƒ(x) = ax2 + 2bx + c with a >0. By considering the minimum, prove that ƒ(x)>= 0 for all…

A: Consider the given function f(x) = ax2+2bx+c with a > 0It is required to prove that:

Q: What is the global minimum of the function f (x) = x/2 (x – 4)?

A: Find the critical points and evaluate the given function at critical point.

Q: 3. The graph of f(x) = 3(x – 2)² – 6 is a parabola that opens %3D with its vertex at (L, -), and…

A: The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If…

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: if f'(x) = x(x-1)(x+3)4 , then f(x) has a local minimum at

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Q: Let g(z) = (- 2)(# - 3)2. Then g has a local maximum at a =

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Q: 1. The graph of f (x) = 2x3 + x² – 20x + 1 has a relative minimum at

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Q: Find the global minimum of the function f (x) = 2x’ + 3x² – 12x + 4 on the interval [-4,2].

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Q: Find the global maximum and global minimum of f(x)=x√x in the interval [2,3].

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Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

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Q: Identify the absolute minimum of g(x)=−2x2 −x+1 over [−2,4].

A: Absolute minimum:The absolute minimum of a function f on the interval [a, b] will occur either at…

Q: The graph of  f(x) = 2(x − 2)2 − 7 is a parabola that opens upwards with its vertex at (x, y) = 2,−7…

A: Consider the graph of f(x) = 2(x − 2)2 – 7

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

A: 9

Q: on a curve is said to be an extremum if it is a local minimum or a local A point maximum. The number…

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

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A: Legranges multiplier

Q: A ship at point A is 50 yards directly north of point C on shore. Point D, also on the shore and due…

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Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: If f'(x) = x(x – 1)(x + 3)*, then f(x) has a local minimum at: Select one: а. х%3-3 only b. x = 0…

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Q: Find the absolute maximum of p(x)=x2 −x+2 over [0,3].

A: We have to find absolute maximum of f(x) in given interval .F(x) is given as:

Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

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Q: Use the first- and second-order optimality conditions to find all local minimums of f : x € R² → ¤1…

A: The given problem can be expressed asMinimize f : x1+3x2Subjected to h : x12-5x22+5 Firstly, we will…

Q: Use calculus to find the x-locations of the local maximum and local minimum values of S(x) = (½)x°…

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Q: If f '(4) = 0 and f '(x) 0 for 4 < x < 5 then f has a local minimum at x = 4. True False

A: If f '(4) = 0 and f '(x) &lt; 0 for 0 &lt; x &lt; 4 and f '(x) &gt; 0 for 4 &lt; x &lt; 5 then f has…

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: 8. Use Lagrange multipliers to determine the absolute maximum and the absolute minimum of f(x, y) =…

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Q: -- ) Determine the values of constanas a, b, c, and d so that f(x) = ax³ + bx² + cx+d has a local…

A: As given (0, 0) is a point of local maximum and (1,−1) is a point of local minimum of f(x). The…

Q: () Determine the points at which fhas a local maximum/local minimum (if any). 4x – 2 f"(x) = (g)…

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Q: (b) Estimate the value of x at whichf has a relative maximum. If there is no relative maximum, 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: What is the local minimum value of the function f(x) = x^3(x + 4)

A: We have the given function as fx=x3x+4 For local maxima/minima, we need to calculate critical point…

Q: Determine where y = x4 - 8x2 has a local maximum or a local minimum.

A: we havefx=x4−8x2

Q: True False  Suppose f(x) satisfies f'(3) = 0 and f"(3)&gt;0, then f(3) must be a local minimum.

A: We will use the second derivative test to answer this. It states that if, at a point x = c, the…

Q: A parabola has x-intercepts of -1, 4, Determine the equation of the parabola in f(x) = a(x-r)(x-s)…

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