Let a > 0 and f(x) = x + . Then ƒ has An absolute maximum at x = -Vā A local minimum at x = Vā A local maximum at x = -a A local minimum at x = a

Q: A function f(t)= 5x + 8x^-1 has one local minimum and one local maximum what is the function has a…

A: Given query is to find the local maximum and the minimum for the function f(x).

Q: Given the function f(x) = (x+3)²(x-1). Find the critical points of f(x) and its increasing and…

A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find…

Q: Given f(x) = ,*, find the critical number(s), the intervals on which the function increases and…

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Q: The function f(x) = xvx – x² defined on the closed domain [0, 0.9] has an absolute minimum value of…

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Q: Find the absolute maximum and minimum values, and the points at which they are achieved, of the…

A: In this, we find the absolute minimum or maximum values ,of the given function.

Q: Let f(x) - (x a) e". Find the local extreme(maximum and minimum) points, where a eR. O a. at x = a-1…

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Q: Let f(x) = 2(x − 1)^2 (2x + 1) be a function. Find all critical numbers of the function and…

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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 absolute maximum and absolute minimum values of f(x) = ! + In r, on [, e²].

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Q: Find the absolute minimum and absolute maximum values of fon the given interval. Rx) = x- In(7x), 2…

A: The given function is fx=x-ln7x,  12,2.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does…

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: If functions f, and g are differentiable, and have a maximum distance between the two functions at…

A: Sure. Happy to help.

Q: Find the absolute maximum and absolute minimumvalues of f on the given interval.   f(x) =5 +54x  -…

A: Absolute maximum or absolute minimum values of a function on the given interval exists at a point at…

Q: 9. Find the local minimum and local maximum values using both the First and Second Derivative…

A: To find the local minimum and local maximum values.

Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

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Q: Find the absolute maximum and absolute minimumvalues of f on the given interval.   f(x) =12 +4x  -…

A: We find the critical points by solving f'(x)=0

Q: find the critical points of f (x) and use the Second Derivative Test (if possible) to determine…

A: Here we will apply first derivative and equate it to 0 to get the critical points and then apply…

Q: Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)). c = Use the Second…

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Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

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Q: Find the (i) local maximum and local minimum values of f (ii) absolute maximum and absolute…

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Q: Let f(x) = e-T". Then f(x) has a relative minimum at -7x² -14xe x = a relative maximum at = x and…

A: We will use first derivative test and second directives test to find the relative maximum minimum…

Q: Let f(x) = e^(2−x^2). Find the x-coordinates of all critical points of the f. Determine whether each…

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Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

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Q: Consider the function f(x) = - 3x+ 2x- 9. f(x) has a critical point at r = A. Find the value of A: A…

A: To find the critical point calculate the derivative and equate to zero than solve for x.

Q: В f has a relative maximum at x = 1. f has neither a relative minimum nor a relative maximum at x =…

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Q: Use the first derivative test to determine the intervals where f(x) is increasing and decreasing and…

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Q: Let f(x)- xx-3 then find the local minimum and local maximum, determine where the function…

A: Given that f(x)=x√(x-3)

Q: Find the critical points and the intervals on which the function f(x) = (x³ - x) e* + 4 is…

A: To find out critical values, take derivative, apply product rule

Q: What is f(x) = x +1/x absolute maximum and absolute minimum at the range [0.2, 4]

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

A: The derivative of the function f is f'(x)=2-3xx+83

Q: Find constants a and b in the function f(x): ar In(x) such that f() = 1 and the function function…

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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: Find the critical points and the intervals on which the function f(x) = (x³ – 4x) e* + 15 is…

A: given f(x)=x3-3247xex +15 we have to find the critical points and the intervals on which the given…

Q: Use a graph of  f to estimate the maximum and minimumvalues. Then find the exact values.(b) Estimate…

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Q: Locate the absolute extrema (maximum AND minimum): f(x) = 10x(2 - lnx) ,  on the interval [1,e^x]

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Q: Can you help me step by step?

A: Since, the function f is an even function, so by definition of even function:

Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

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Q: Find the absolute maximum and absolute minimum valu nty=t-Vt, [-1, 5]

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Q: A continuous function, h(x) has a local maximum at (2, 3). What is h’(2)?

A: We have given that h(x)  is a continuous function and has a local maximum at point (2,3).

Q: The function f(x) = 1+x has a local minimum when a = 0. Select one: O True O False

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Q: f(x)=12+4x-X ', [o,s]

A: We will use derivative test to find the maxima and minima.

Q: 2. Consider a function f : R → R where S(x) = x³ – 3x for all æ e R. Identify all critical points…

A: Given the function fx=x3-3x  ,x∈R. To find the critical points and the local maximum and local…

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: f(x) = 2x² - e²

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Q: Find the absolute maximum and absolute minimumvalues of f on the given interval.   f(x) =(x2 - 1)3…

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