1. Find the maximum value of the function f(x.y)= 4x + 2y +x* - 2x*+ 2xy– 3y° on the interval –2 to 2 for both x and y employing the specified method below: (a) random search method using google sheet or excel with 500 iterations. (b) equating each partial derivative offwith respect to x and partial derivative of f with respect to y to zero, and then solve the nonlinear system of equations using fixed-point iteration or Newton's Method. (c) random search method using a program that you created.

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: Use the first derivatives to find the local exterme of f(x) =x³ -12x on R

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Q: Q1) Find the Derivative to the function and find local minimum and local maximum points y = 3x? - 3

A: y=3x2-3 We need to find the derivative of the function and to find the local minimum and local…

Q: 4. Using the first derivative test to find the location of the local maxima of the following…

A: Given function is  f(x)= x^3 -3x^2 -9x-1

Q: 3. Find the points (x,y) of the function f(x) = -x³ + 12x² - 5 where the tangent is horizontal AND…

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Q: Find the derivative of the following function. y = In(6x² – 7x) – 4x А) 18х? -7х x(6х* - 7) В) 1 - 4…

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

A:

Q: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: 6x erivative of f(x) equal to zero, calculate x*: f'(x*) = 0. Using the second derivative ther x* is…

A:

Q: (a) f(xi), f(xi+1) and f(x+2) are three data points of f(x) and equally spaced at x with the step…

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Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: f(x) = (4x² + 3x)² h(x) = 7 (4x³ - 6x²)³ b) d) g(x)=√10x² - 5x y = 1 3/(x ³√(x + + 5)²

A: We have to find out derivative for different functions.

Q: The amount, A, of anesthetics that a certain hospital uses each week is a function of the number, S,…

A: It is given that;  The amount, A, of anesthetics that a certain hospital uses each week is a…

Q: Find the derivative of the following: a.) f(x) = 5x6 +- 3x3/5 x3 b.) f(x) = (x' + 4x)(x5 – 2) (Hint:…

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Q: The temperature of a chemical reaction oscilates between a low of 25 C and a high ot 120 C. The…

A: Let's find.

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: Do you notice anything surprising? Cân you make a conjecture? (c) Now use the derivative and the…

A: Statement : A small change in your average gas mileage (in miles/gallon) change the number of…

Q: 3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d dx |x| b) Sketch the graphs of…

A: We will use the give solution as we are instructed.