Find the absolute maximum and absolute minimum  of f(x)=e−2xf(x)=e−2x  over the interval [−1,3][−1,3].

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

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A: take the partial derivative with respect to x

Q: Given f(x, y) = 2x3 – 3y? – 6xy %3D (i) Find critical points of f. (ii) Use the second derivative…

A: Given that,f(x, y)=2x3-3y2-6xy-12x

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Q: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

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A: We have given functions fx,y=x2+y2   and gx,y=x2-y2 We have given 0,0 is a critical point of these…

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

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

Q: Find the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]

A: We find f'(x) using chain rule

Q: In the function:  f(x)= (3x^2)ln(x) , x>0  What are the critical numbers of the function?

A: Given function is

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Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

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Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

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

A: To find: The maximum and minimum value of the below function in the interval [-1/2, 1].

Q: Find and classify all critical points of each of the function: a.f (x, y) = (x² +x + 1)e¬²/10-y² f…

A: Solution is given below:

Q: Find the maximum and minimum values of the function f(x, y) = e²Y subject to + y° = 16

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

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Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: II- Find the local maximum and minimum values and saddle points of the 3y? 3xy - 2 function f(x, y)…

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Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

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: find the minimum and maximum value of the function on. the given interval by comparing values at the…

A: Given function is Firstly, we find critical points of y=f(x)  Also, given function is defined for…

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

A: We find y' using the quotient rule

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

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: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

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

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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: For the function f(x,y)=x^2+2y^2−(x^2)y, does the critical point (−2,1) correspond to a local…

A: Given,  Critical Point: (-2, 1)

Q: 6. For the function y=x³, is x=0 both an inflection point and a local maximum /minimum?

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Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: Find the local minimum value of f(, y) = 4+ x1 + yl – 11xy.

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Find the maxima and  minima using second derivative test

Q: Let f (x, y) = x3 – 3xy + y3. Find all critical points of f and at each critical point, - use the…

A: Critical points using second derivative test

Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

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