Let C be a real number and let f(x) = - - 6C. If the slope of the tangent 3 2 line to the graph of f(x) at its inflection point is -108 then find the local minimum value of f(x).

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: Q1- Find any local maximum and local minimum values and sketch the curve: x? + 1 f(x) x2 – 1

A: Sketching curve and finding extremums.

Q: Let C be a real number and let f(x) 5C. If the slope of the 2 3 tangent line to the graph of f(x) at…

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Q: Ca Let C be a real number and let f(x) = 3 .If the slope of the tangent line to the graph of f(x) at…

A: Given that the function fx=Cx33-8Cx22. The derivative of the function fx=Cx33-8Cx22  is…

Q: If  P=27/47 +r2 , determine the value of r for which P will be a minimum. Use the second derivative…

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Q: Let C be a real number and let f(x) = 3 70 . If the slope of the tangent line to the graph of f(x)…

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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: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Lef x, ---Xn iid uCo, @) find minimum Safficient

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Q: Find the local minimum value of f(x, y) = 4 + x° + y° – 9xy. ::

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Q: Q1- Find any local maximum and local minimum values and sketch the curve: x? + 1 f(x) = x2. - 1

A: Given that  f(x)=(x^2+1)/(x^2-1) To find the local maximum and local minimum

Q: Suppose f'(x) =x++x³ – 6x². Determine the value of x where f has a relative minimum value.

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Q: Findthe absolute minimum on ico, ae) fon f (x) =x+l6,

A: Critical points of the given function can be found if dfdx=0 fx=x+16x Differentiating the function…

Q: Find the local minimum value of f(æ, y) = 4 + x7 + y7 – 7xy.

A: We need to find the local minimum value of f(x,y)=4+x7+y7-7xy.  For this we find the partial…

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

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Q: Find the local minimum value of f(r, y) = 4 + x7 + y7 – 7ry.

A: We have to find the local minimum of the function f(x,y).

Q: Let f (x)=x* + 2.x³ – 3.x² – 4.x + 4. Find: (b).. the points at which f (x) has a relative maximum…

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Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: At what value of x is f minimum?

A: To find: The value of x for which f is minimum. Calculation: It is observed from the graph that the…

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

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Q: Give the intervals of increase and decrease of f(x), give the local minimum values of f(x), and give…

A: Given : The function given is f(x)=x+6x23. Differentiate the function with respect to x.…

Q: 2. Find the minimum value of f(x) = %3D

A: We expert are supposed to do first question . We have to find minimum value

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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: Find the local minimum value of f(x, y) = 4 + x15 + y!5 – 15xy.

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Q: Find the absolute minimum value of the function   g(x)  = ex/x, x>0

A: The function is gx=exx for x > 0.   Differentiate the function with respect to x.…

Q: Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative minimum value.

A: Explanation of the answer is as follows

Q: Find the local minimum value of f(x,y) = 4+ x11 + y11 11zy. %3D

A: We have to find the local minimum value of the function f(x,y).

Q: Find the local minimum value of f(x, y) = 4 + x11 + yll – 11xy.

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Q: Use the graph to state the absolute and local maximumand minimum values of the function.

A: Absolute maximum value= 5  Absolute minimum value= None (because there is an open circle at the…

Q: For y> 0, find the minimum value of + 10 +5y2 5 y2

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Q: Given f (x)= (x^2) (e^-x) , find the relative maximum and relative minimum point respectively.

A: We will use derivative to find maximum and minimum value for the function. If f(x) is a function.…

Q: Find the relative minimum f(x,y)=288y2+x2-x2y

A: According to the given information it is requires to find the relative minimum of the function:

Q: Find the values of constants a, b, and c so that the graph of y = (x2 + a)/(bx + c) has a local…

A: given

Q: Find the value of a necessary for there to be a local minimum at x = 2 for the function f(x) = -ax²…

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Q: Find the local minimum value of f(x, y) = 4 + x'l + yll - 11xy.

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Q: Find the absolute minimum value of the function f(x) = et (0, 0). on

A: Given function f(x) = exx    on   0 , ∞

Q: Let A be a positive real number. If the absolute minimum value of  f(x)=Ax^5−25x^3 on [0,∞) occurs…

A: A be a positive real number.  absolute minimum value of f(x) where  f(x)=Ax^5−25x^3 on [0,∞) occurs…

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A: Given:                          fx=x+1x Differentiate f(x) with respect to x…

Q: If f'(x)=x^3-2x^2-x+2, then f has a relative minimum at x=

A: If f'(x)=x3-2x2-x+2, then f has relative minimum at x

Q: 2) Find the absolute minimum value on (0,∞ ) for 4 f(x)= 5+x+

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

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: If the graph of f has a horizontal tangent line at x = c and f" (c) is negative, which of the…

A: The graph of f has a horizontal tangent line at x=c and f''c is negative

Q: Find the point on the line y = x that is closest to the point  (3, 1).[Hint: Express the distance d…

A: Assume d be the distance from point y=x to the line y=x Assume (x,y) be a point on a line ⇒(x,y)…

Q: Find the absolute minimum value on​ [0,∞​) for f(x) = 2x2 -12x + 6

A: To find the absolute minimum value of the function on the given interval.

Q: (b) Estimate the value of x at whichf has a relative maximum. If there is no relative maximum, enter…

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