he graph of a function fis shown below. ind one value of x for which f(x) = 4 and find f(2). %3D

Q: k does the graph or f(x) use it to justify your reas

A: f'(x)=-2x(x-3)2 We need to integrate the above function.f(x)=∫-2x(x-3)2dxf'(x)=-2x(x2-6x+9)…

Q: The function f(x) is graphed below. How many points on the graph represent a relative extreme value?…

A: Relative extreme values occurs at the points where slope of the tangent of the graph at that…

Q: The graph below is the function f(x)

A:

Q: Give the equation for the function whose graph appears above. Use f(z) as the output. Question Help…

A:

Q: ind the points on the graph of the function that are closest to the given pe f(x) = x², (0, 6) x, y)…

A: Given function is fx=x2 To find the point on the graph of f(x) that is closest to the point (0, 6).

Q: Write an equation for a function that has a graph with the given characteristics. The shape of y= Va…

A: If a function is reflected across the y axis then we write -x in place of x.

Q: Use the graph of y = f(x) to answer the question regarding the function. Step 3 of 4: Find f(-1).…

A: We have to find the function value

Q: Please see attached.

A:

Q: Use the graph to answer the following questions. (refer to image) (g) What is (f◦g−1)(5) (h) Solve…

A: 1.) ( f • g -1 )(5) = f( g -1(5) ) = f( 4 ) = -2. as from the graph g(4) = 5 so g -1(5) = 4 .

Q: A graphing calculator is recommended. Use a graph to estimate the values of x such that ex > 1,000.…

A: topic - Inequality

Q: Graph the function f(x) = 2(7)* by hand. Then use a graphing calculator to verify your graph. Choose…

A: In this question we have to find which graph is best suitable for given equation.

Q: 7. The graph of f(x) is shown below. Solve f(x) < 0.

A: Note that fx less than zero, means that the function will be below the x-axis. That is , it is…

Q: The function f (x) is graphed below. How many points on the graph represent a relative extreme…

A:

Q: b. Identify the function's local and absolute extreme values, if any, saying where they occur.

A: For The graph of a function y = f(x)  The local maximum occurs at the point where the graph changes…

Q: Q Find the omain and the range and sketch the graph oF each Hhe fallowing Function? 2X+3 if Xン

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Q: Find a possible formula for the function whose graph is pictured below. You do not need to multiply…

A: From the graph we can see that the x-intercepts are -1, 0, 1, 0 &amp; 2, 0. Therefore the factors…

Q: (a) sketch the graph of the function f(x)=x|x| (b) for what values of x is f differentiable? (c)…

A: The given function y=x|x| can be written as,

Q: 6. Graph the following and answer the following questions. x² frx) = 2- メ22 Function? Yes or No…

A: Given function is, fx=x2, x&lt;2-x ,x≥2.

Q: The graph of f(x) is given below.

A: Given that: Graph of f(x)

Q: A D C Graph of f

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Q: tind the widest range of t Function? 水十さスー10

A: Given function is y=2x2+2x-1x2+3x-10 find the range of the function

Q: LThe graph of a function f(x) is shown below. What is the value o fx) dl

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Q: alue over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent…

A: Introduction: Exponents are used in the exponential function, as the name implies. However, an…

Q: The graph of a function y = f(x) is shown. At which point(s) are the following true? (Select all…

A: We have to select option.

Q: 3. Graph the function. S(x) = 2\=

A: We use the graphical analysis in order to solve the given problem.

Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

A: The f(x) has a horizontal tangent where the slope of the curve changes.

Q: y = S(x)

A: Consider the given figure:  a) Draw the tangent line to the graph of f at x = 0. The derivative of…

Q: The graph of a function y = f(x) is shown below. Estimate a value of æ such that f(x) = 5. 16 10

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Q: 5. Graph the following and answer the following questions. { -3 メ43 frx) = x >3 Function ? Yes or No…

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Q: 5 10pi 10pi -5

A: we know that the graphing function of sine . y =A• sin( B ( x + C )) + D Here | A | = amplitude . C…

Q: Consider the graph of f'(x). Where are the inflection points? Where is the graph concave up/down? -2

A: A inflection point in a graph is the point where the graph changes from concave upward to concave…

Q: E212 Me whether the smt te The following graph is a function?

A: In the question it is asked to find whether the given graph represents a function or not.

Q: Using the graph above, state where f (x ) (d) has relative extrema: (e) is concave up: (f) is…

A: Relative extrema of a function are the points on the graph of the function where it has a local…

Q: Write a formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 5 units…

A: We can use the concept function transformation.

Q: Let f(x) = a? If g(z) is the graph of f(x) shifted up 5 units, write a formula for g(z) g(1)=…

A: The detailed solution mentioned in the step 2.  g(x) = f(x) + 5  g(x) = x^2 + 5

Q: Use the graph of y = f(x) to answer the question regarding the function. Step 3 of 4: Find f(-2).…

A:

Q: Let f(x) be the function graphed below. Solve: (a) f(x) >0 (b) f(x) Next Question

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Q: 3. Find the range of the function below.

A: Given,          The graph of the function is shown below :

Q: In Exercises, which of the graphs are graphs of functions of x, and which are not? Give reasons for…

A: There is a vertical line test to check whether a given graph is of a function. Imagine a vertical…

Q: The graph of the function y=f(x) is given below. Find the range of f(x). Give your answer in…

A: Given is

Q: The graph of the function y= f (x) is shown. 24. Which of the following sketches illustrates th…

A: Given function is y=f(x). We know that graph of function y=f(-x) is the reflection of graph about…

Q: Find a possible formula for the trig function graphed below. Use x as the independent variable in…

A: to determine the trigonometric function for the graph.

Q: 10. Which graph represents the function f(x) = 2sin(30)? New version a

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Q: In the graph below. Two functions n(x) and j(x) are graphed. Find the following:

A: Given: The graph of parabola and a line.

Q: The function f(x) is graphed below. How many points on the graph represent a relative minimum? a b f

A: Given, The graph of the function fx We have to find how many points on the graph represents a…

Q: —х — 2, х < -2 V9 — х?, —2 <x<1 3 — х?,1 <х | 2) f(x) =

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Q: y = f(z)

A: By finding out the slope of the function at point we can draw derivative function

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.