2. Let f(x) = r² – 6r – 7 a) Find the critical numbers of the function. Show clearly and specifically which of the criteria is met to warramnt the classification as critical mumber. b) Find the absolute maximum and minimum values of the function on the interval [0, 5]. Give both simplified, exact values as well as approximations to the nearest tenth.

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Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.

Q: 5. If c is a critical point of F(x), when the is a local maximum or minimum at c? Explain

A:

Q: 8:(- 2, 2]– R, g(x) = [* (1 - 3)(r² + 1)dt L (1- 3)(*' + 1)dt

A: Answer is given in next step.

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Q: :(- 2,2]– R, F(x) = L(-3(² + 1) dt

A: Given data :  F(x)=∫-2x2(t-3)(t2+1)dt

Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: Given a function f ( x, y) = x3 + y3 + 3x2 -18y2 + 81y + 5 The function has four critical points…

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Q: 2. Let f(x, y) = (x² + y²)e-. Find and classify all of the critical points.

A:

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Q: - y = In(x – 2)

A:

Q: 3. Let f(x) = 2x In(x). 3.1. Determine all the critical numbers to f(x). 3.2. For each critical…

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Q: 8. Determine if the critical point (0,0) of f(x,y) =x³+2xy² – y4 +x² + 3xy+y² +10 is a local…

A: f(x,y) = x3 + 2xy2 - y4 + x2 + 3xy + y2 + 10 => fx = 3x2 + 2y2 + 2x + 3y      fxx = 6x + 2…

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Q: 1. Find the critical numbers of the following function. f(x) = x-v*(x – 2)

A:

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Q: 1. The following questions refer to Figure 15. (a) How many critical points does f have on [0, 8]?…

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A:

Q: 5. Ifc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

A: To give the condition of local maximum or minimum at c if c is a critical point of F(x).

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Q: Let f (x, y) = y - 8ry + 2x? – 3y + 4x - 23 . Find all critical values for this function and…

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Q: Find and classify all the critical points of f(x, y) = x³ - y³ - 8xy.

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Q: 26 a. The function f(x)=x- 6x² + 9x-3 is defined on the interval [0,5]. Find the critical points of…

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Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

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Q: For a function f(x,y), suppose that fxx 3x2 and D(x,y) = fxxfyy-fxyfxy 4y- 12. Which is true for the…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.