The absolute Extrema of the function f(x) = –x^2/3onthe interval (-8, 0 )are

Q: how do you find the tangent line to the curve of f(x)= -6 square root x at x=4

A: We have given,

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

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Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=6…

A: Given:            fx=6x-x2 Second derivative test definition: Suppose that x = c is a critical point…

Q: Describe the First Derivative Theorem for Local Extreme Values?

A: Describe the First Derivative Theorem for Local Extreme Values?

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16…

A: The tangent line is horizontal where y'=0

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: why first derivative is zero at local maximum and local minimum of function in an open interval

A: The first derivative is zero at local maximum and local minimum of function in an open interval…

Q: The second derivative of function: Inesina will be Select one: O sina O -sinz

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Q: What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.

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Q: The function has only one critical point at x = VIn(a). Use the Second Derivative test to identify…

A: Solve g'(x)=0 to obtain the critical points. Then evaluate g'' at those critical points. If it is…

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: The second derivative test fails when f" is zero or does not exist at the critical number of the…

A: Given data: The value of the second derivative of the function is f''=0.  Suppose at the given point…

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2 x2 + 3x using First…

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Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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Q: 1 F(x) = -1. tanh 3x

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Use Intermediate Value Theorem to show that the equation

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Q: Explain theorem 10—First Derivative Test for Local Extreme Values?

A: According to the question, we have to expalin the theorem for first derivative test for local…

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: find tangent line to the curve y=3x/7-x at a point of (-3,2/7)

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Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: At critical points the first derivative of the function will be zero , Second derivative test At…

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

Q: Find all relative extrema of the function f(x) = x² - 4x² + 2 by using the Second Derivative Test…

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Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

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Q: f(x) = - sin(2x) on the interval TC

A: f is maximum at x = - π/4 f is minimum at x = π/4   The detailed solution is as follows below:

Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: 5. Use the Second Derivative Test to find all local extrema of the function below. (3 points total)…

A: To find the local extrema of the given function f(x)=x4-4x3+2

Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.