Consider the function f(x)=5x^2−40x on the interval [0,5]. Find the absolute extrema for the function on the given interval. Express your answer as an ordered pair (x,f(x)).

Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: 1. Given: x3+y3=6xy To find y'by using implicit differentiation the implicit differentiation is…

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

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Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Using the Constant Multiple Rule InExercises 25–30, complete the table to find thederivative of the…

A: The given function is, y=5x2-34. The objective is to find the derivative of the function by using…

Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: 0 and f'(x) > 2 for 1sxs4, how small can

A: It is given that f(1)=10, f'(x)≥2 for 1≤x≤4.

Q: Q-3-Edaluate the fallowing Integration 1- X3 x21 2. 2- X+1

A: Use the partial fraction to solve the given problem.

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A: Given that,The path of a basketball is given byy=2.12+2.01x-0.38x2, 0≤x≤4.6wherex is the horizontal…

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A: We have given that in the basketball game ,the ball travels the path given by y=2.15+2.09x-0.41x2…

Q: f(x) = (6x² - 2x+1)^

A:

Q: The firm is very interested in maximizing profits. Its profit model is given by the function: f(x) =…

A: Solution is given below:

Q: An ant is standing at the point (1,1,3) on the surface of a bowl with equationz=x^2+…

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Q: Use Milne's method to obtain the value of y(0-3).

A:

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

A:

Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: 1 F(x) = -1. tanh 3x

A:

Q: The maximum value of y = cos x for - < x< is 1

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Differentiate the function y=sinx2+3x3.

A: Given: y=sinx2+3x3 we know that ddxsinx=cosxddxxn=nxn-1

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Given the function y = 8e-2x + 7 sec² 5x - 4 ln x³, find y'. Solution: 4(3)x² 3 12 X ------- 12 1…

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Q: ) Find the integration: V1-X

A: Given integration, ∫032dx1-x2

Q: An object is projected upward from ground level with an initial velocity of 500 feet per second. In…

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

A:

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: Consider f (x) = x* – 8x2 + 1. a. Find the critical values. b. Use the first derivative test to…

A: We have , f(x) = x4 - 8x2 + 1.  To find : Critical Values.

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A:

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: Find 2 at the point (4,1,6) for -6x² + 7 ln xz + 4yz² – 2e? = 0 %3D

A:

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Find y" by implicit differentiation. 3x" + 4y - 2

A: differentiate it with respect to x.

Q: Solves methad of vriation of Parameters - secx by the yot gosx +イne

A: We use the method of variation of parameters to solve this problem.

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

A:

Q: A golfer makes a successful chip shot to the green. Suppose that the path of the ball from the…

A: Please refer to the image below

Q: Find y ' by implicit differentiation for 4x² y7 – 2x = x5 + 4y3 . %3D

A: We have to find y' by implicit differentiation of : 4x2y7 - 2x = x5 + 4y3

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: Differentiate f(x)= (3x+2)^(arctan(x))

A: We can solve this problem using logarithmic derivative.

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A:

Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

A: