For what values of a is the graph of y = xe -2x concave down? values =

Q: For the function y=x-1, graph the points with the domain of {0,4,6,8,9}

A: Domain: Set of values of x or independent variable for which the value of y or dependent variable…

Q: I need help graphing f(x)= 1/2x +1 and g(×)= -|x-2|+5 Y= F(×) as a line Y= G(×) as 2 ray segments

A: Given function f(x)=12x+1 Since, graph of function h(x)=1x is hyperbolic shaped. To obtain 'f(x)'…

Q: b. Find the slope of the curve at the given point. y* = 2x; (648,6)

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Q: For what values of x is the graph of y = re concave down?

A: Given function, y=xe-4x The graph of y=f(x)  is concave down on the intervals where  f''(x)<0 Use…

Q: y -1 1 2 4 3,

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Q: H.w.cl) Q,- Graph the function y= 2

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Q: find the domain and Range for the functions FCx) from the graph below! y, 3 -2 • 3 1

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Q: In the above graph of y = f( x ), find the slope of the secant line through the points (-1, f( -1) )…

A: Given co-ordinate of secant line are p-1,f-1 and Q 1,f1  from graph f-1=-2                      f…

Q: Sketch the graph and determine the domain and range. 1. y = 2 - x, for x 2-4 2. y= x? - 6x + 5, for…

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Q: (a) Find the points of inflexion of the curve y(a² +x²) = x³

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Q: a. d. 1 =x+2 y = 1 --x+2 y = -x + 2 * 1/2x-2

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Q: find the slope of the curve at the point indicated y = 5x - 3x2, x = 1

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Q: By experimentation, determine the approximate value of a (where 3 < a < 4) at which the graph…

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Q: Trace the curve x^3 − 6x^2 + 11x − y = 6.

A: Given- x3-6x2+11x-y=6 To draw- The graph of the above function. Concept used- The above expression…

Q: Find the equation of the curve that passes through (- 2, – 30) if its slope is given by oy = 9x2 -…

A: The slope of the given curve is given as dydx=9x2-8x and point passes through is -2, -30. To find :…

Q: Find all points on the circle x2 + y2 = 100 where the slope is 3/4.

A: Given equation of circle, x2+y2=100                          ...(1)

Q: Find the slope of the curve y = 2x* + 3x + 2x? - 1 at a point where it crosses the x-axis

A: The point where y crosses x-axis the value for y is 0. Find the value for x for which y = 0.…

Q: What will be the x-coordinate of Point C?

A: I have given an answer in step 2.

Q: find (y" ) for the following equation 3x²-2y'-y=6 at point (2,1)

A: Take the first derivative of the whole term than find y' at given point after this calculate second…

Q: Use the graph of y=f(x) to answer the following. y 4. 3+ 2+ -3 -2 3 -2- -3- -1

A: We can find the domain and range as below.

Q: Find the point on the graph of y = x2 where the curve has slope -6.

A: Given curve is y=x2. To find the point on the graph of given curve where the slope is -6. Solution:…

Q: Determine the slope of the graph of 3(x2 + y2)2 = 100xy at the point (3, 1).

A: Given: 3x2+y22=100xy we know that slopem at given pointx1,y1 is given by m=dydx|x1,y1 so, we…

Q: Let c be a fixed constant. Explain the relationship betweenthe graphs of: y = f (x + c) and y = f…

A: To explain: The relation between the graphs of y=fx+c and y=fx in rectangular coordinates. Concept…

Q: Find the point(s) on the graph of y = (2x4 + 1)(x - 5) where the slope is 1.

A: Our Aim is to find the point on the graph of y=(2x4+1)(x-5) where we have slope=1

Q: fird the equation of the fangent lineto the graph of Y= ☆ at X=2

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Q: Sketch the graph of y = f(x). е.

A: The graph of y=f(x) will be

Q: For what values of x is the graph of y=xe^(−2x) concave down?

A: Find first derivative using product rule and chain rule.

Q: Trace the curve: y= x / (x-1) (x+3)

A: Consider the given function y=xx-1x+3

Q: Find all points on the circle x2 + y2 = 100 where the slope is 3/4

A: Given circle x2+y2=100 .....(1)  where the slope is 34we have to find all points on the circle

Q: In the above graph of y=f(x), find the slope of the secant line through the points (−4,f(−4)) and…

A: Slope of the  line passing through (x1,y1)  and (x2,y2) is (m)=∆y/∆x= y2-y1/x2-x1

Q: find the slope of the curve at the point indicated.

A: We have to find out the slope of the curve at the given point. y=1x-1 , x=3 for the slope we have to…

Q: What's the relationship between (x)^1/2 and (x)^2? Based on their properties and graphs

A: whats the relationship between the given curve

Q: At what point of the curve y = x3 + 3x are the values of y’ and y” equal?

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Q: Find the slope of the curve at the indicated point. y = x2 + 3x - 5, x = 2 O m = 7 O m = 2 m = 10…

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Q: Find the point(s) on the graph of y = (x^2 + 3x − 1)/x where the slope is 5

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Q: The level curves of the function f (x, y) = /2x2 + y? – 1 are

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Q: The graph of y-Jx) is shown. HS4 2 3 4 5 -2 -3 Evaluate x when x) 4

A: The graph of the function f(x) is shown below:

Q: How does the value of a affect the graph of y = ax? Discuss the case for a 1 and for 0 s a s 1.

A: When a &gt;=1  Graph will shrink towards y axis that is value of y increases more rapidly When 0…

Q: For what values of x is the graph of y = e concave down?

A:

Q: The graphs of x = 4, y = f(x) (s

A: Volume =∫ab A(x) dxA(x) = π[(Outer radius)2-(Inner radius)2]

Q: In the above graph of y = f( x ), find the slope of the secant line through the points ( -4, f( -4 )…

A: The solution for the above question is as shown below.

Q: Find the point in the curve y = x³ + 3x for which y' = y'

A: Roots of y' problem....

Q: Find a function whose graph is the given curve. The top half of the circle x2 + y2 = 9

A: Given  The top half of the circle x2+y2=9 To find a function whose graph is the given curve. The…

Q: Find the slope of the curve at the given point. y=2x^3−3x @ (-1,1)

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Q: Given the graph of y = f(x) below, what is the range of y = f(x) – 2?

A: The graph of y=fx is given. We have to determine the range of y=fx-2

Q: Which of the following is the y-coordinate for the point that lies on the line y=-3/4x+1 and has an…

A: substitute the  value of x .

Q: For what values of a and b the point (−1,2) is an inflection point of the graph of the function…

A: As (2,-1) is a point of inflection, it must satisfy the equation of function. Substitute x=-1 and…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.