Find all the local maxima, local minima, and saddle points of the function. f(x, y) = 5 2 2 x² + y²-1

Q: Write the expression as a single logarithm. 7 log 5u + 8 log 5v 7 log su +8 log 5 v= (Simplify your…

A: The given expression is:

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Q: A company produces handmade shawls and afghans. They spin the yarn, dye it, and then weave it. A…

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Q: Suppose f(x), g(x), and h(x) are continuous functions such that g(-1) = 4, h(-1)=3 and lim…

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Q: 不 Suppose that you decide to buy a car for $50,000, including taxes and license fees. You saved…

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Q: Consider the function. f(x)=x²-1 (a) Find the inverse function of f. f-¹(x)=√√x+1 (b) Graph f and…

A: The function is given byThe inverse function is

Q: y subject to the constraint x² + y² 4. Find the relative extrema of f (x, y) = 4x3 + y² subject to…

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Q: Use derivative rules to differentiate the function. Perform reasonable simplifications. f(y) = tan…

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Q: 4. A coffee shop currently sells 480 lattes a day at $3.00 each. They recently tried raising the…

A: Given that coffee shop sells 480 lattes a day at $3.00.As given let x= number of $0.60 increase in…

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line to the curve at the given…

Q: Find Proof for Derivative Formula f'(x) = lim f(x tb) -f(x) h

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Q: Sometimes a change of variable can be used to convert a differential equation y' = f(t, y) into a…

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Q: Suppose that In 5= a and In 11 = b. Use properties of logarithms to write the logarithm in terms of…

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Q: Could the function in the bottom plot be the derivative of the function in the top plot? Explain…

A: We have given two graphs and we have to explain if function in bottom plot could be derivative of…

Q: 1. Differentiate the following equations. a. b. C. d. e. Differentiate. f'(x) = Differentiate. f'(x)…

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Q: The liquid base of an ice cream has an initial temperature of 93°C before it is placed in a freezer…

A: By Newton's cooling law k=Proportionality constant surrounding temperature temperature of an object…

Q: Find f'(x). f'(x) = f(x) = ex - 5x Compare the graphs of f and f' and use them to explain why your…

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Q: Question 5 7 Let f (x) X The slope of the tangent line to the graph of f (x) at the point The…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → 00. lim n→∞ i = 1 5…

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Q: Find equations of the tangent line and normal line to the given curve at the specified point. y =…

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Q: lf f(x) = x sin(2x), evaluate ƒ''(7). 2 ƒ'' (-/-) =

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Q: Computed using the chain rule if dx 2u5 - 3u³ +u+1 y U = = and u² - 2u³ + 3u² (x² − 1)(3x² + 2x + 1)

A: given  and

Q: A particle moves on a horizontal line so that its position, in centimeters, at time t, in seconds,…

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Q: You deposit a lump sum Pin a tnast fund on the day your child is born. The fund earns 7.3% interest…

A: Rate of interest  r=7.5%=0.075future value  A=$ 600,000

Q: An offshore oil well is 2 kilometers off the coast. The refinery is 5 kilometers down the coast (see…

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Q: +¹) (y +ı) ex dy x y ³ dx + (y X = 0 1 = 6

A: The given differential equation is

Q: Sketch the graph of. f and use your sketch to find the absolute and local maximum and minimum values…

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Q: 3. xy³ dx + ex" dy = 0 te x = 0 y = 2

A: To solve the following differntial equation.

Q: Does this fuction have a minimum value?

A: The function Let

Q: Using the definition to proof a derivative formula f'(x) = lim, to f(x+h)-f(x) h

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Q: O O O 1. Write the function f(x) = value symbols). f(x) = { f(x) = - 10 x +8 as a piecewise function…

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Q: Find the higher order derivative. f'(x) = 4x² + 4x - 16 f(5) (x) = X

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Q: Find #f dy dt dt if y= 2 u+u and u= 14 +5t.

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Q: (x) f'(x) g'(x) f"(x) 1 2 0 1 X). -1 3 -2 4 4 -2 3 2 3 ). pe of y(x) at x = 0. -4 1 2 -9 ave a…

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Q: The California Almond Growers have at most 3200 boxes of almonds to be shipped from their plant in…

A: Let x be the number of boxes to be shipped to Des MoinesLet y be the number of boxes to be shipped…

Q: 5)(x + 5)(x − 5) Enter your answers as a comma-separated list.

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Q: The pollution on a beach can be reduced to half of its previous level with each day it is cleaned.…

A: The pollution on a beach can be reduced to half of its previos level with each day it is cleaned. To…

Q: Find the Riemann sum for f(x) = x² + 3x over the interval [0, 8] (see figure), where Xo = 0, X₁ = 1,…

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Q: Use derivative rules to differentiate the function. Perform reasonable simplifications. h(x) 8x +…

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Q: The radius of a spherical balloon is measured to be 7 inches,

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Q: Find the saddle point(s) of the function:  f(x,y) = 2x3 - 6x + 6xy2

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Q: f(x)=√√4x² +2

A: f(x)=4x2+2

Q: Differentiate. f'(t) f(t) cot(t) e e¹(cot(t) + csc(t)²) X

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Q: Use the graph of the function f(x) shown below in order to determine all values of x in the interval…

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Q: 2. Differentiate the following equations. a. b. C. d. 9. h. f'(x) = f'(t) = f'(x)= F'(t) = A'(s) =…

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Q: Find the values of m and b that make f continuous everywhere: 54+3x-² x+6 mx + b 4.24 +51 f(x) =…

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Q: (d) 108 [² f(x) dx Enhanced Feedback Please try again. To evaluate an integral by interpreting it in…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in  the…

A: Find the volume of the largest rectangular box in the first octant with three faces in  the…

Q: Find the slope of the curve to: 4 where x=2 - 2x³ 3x² + 5x + 9 at the point

A: Let,