Sketch a graph with the following properties: f(0)=f(6)=0, f(3)=2 f'(3)=f'(5)=0 f'(x)>0 if x<3 or 35 f"(x)<0 if x<3 or x>4 f"(x)>0 if 3

Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

A: Given that the first derivative of the function is  y'=(8x-5x2)(4-x)2

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Q: Find the 1st derivative y=(x-1V2x-x t arcsin (x-1)

A: I am attaching image so that you understand each and every step.

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A: To determine: The local maxima point.

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Q: 1 Find the derivative of f(x) = - at x= 3 %3D (Type an integer or a simplified fractic 21 %3D

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Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

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Q: Determine the coordinates of the point(s) on the graph of f(x) = 5x ^3 - 2x ^2 where the tangent…

A: Our aim is to determine the coordinates of the points on the graph off(x)=5x3-2x2 where the tangent…

Q: Ex.2 : Use first derivative , second derivative, and the graph y= x²-4 to asymptotes X-1

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Q: Find the critical points of the following function on the given interval. Identify the absolute…

A: The given function is, ƒ(x) = x3 ln x  The interval of the function is (0, ∞) The critical point of…

Q: draw a graph to match the description given.  f(x) has a negative derivative over (-infinity, 2) and…

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A: To find the intervals of increasing and decreasing

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Q: determine all critical points and all domainendpoints for each function. y = ln (x + 1) - tan-1 x

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Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=xlnx Differentiating with respect to x, we get f/x=dxdxlnx+dlnxdxx    Because,…

Q: # 22 A right circular cone of radius 6m and height 10m is initially filled with water. An empty…

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Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: first derivatives test to find local exterma of f( x) =x3 -12x on R

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A: Given,                 f(x)=5sin(2x)-2x2 and  initial guess of x = -0.38.

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A: To find the root of the below function near x=4.5. fx=2x−secx−3+1

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A: A function is increasing, if when x increases, the value of y also increases.          Since the…

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Q: Limit x approaches to + infinity 3x+1 ÷ 2x-5

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Q: (b) Use both the first and second derivative tests to show that g(x) = 2tan²x has a relative minimum…

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Q: Find the second derivative y=5e^x -2/x^3 +4sqrt(x) -12sec x + 5lnx - pi/2= Find equation of tangent…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.