Your Turn The graph of a reciprocal function of the form y = = 1 where a f(x) ax + b' and b are non-zero constants, is shown. 6 -4 2 (-2-3). a) Sketch the graph of the original function, y = f(x). b) Determine the original function, y = f(x). -12

Q: Find the derivative of the function. 6x3 f(x) = + 8x2 Step 1 The function (x) can be simplified to…

A: The differentiation is given below.

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A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: Choose the correct equation for the function shown in the graph. yA - 47 21 21 471 X -1 y= sin y=…

A: The given graph is

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A: Given  f(x) = 16-6x2-23 We have to find the equation of the tangent line to the graph of f at the…

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A: Given,fx=x3-2x2-10sin2x-e0.9xf'x=3x2-4x-20sinxcosx-e0.9x· 0.9

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A: We will find the first order partial derivatives and use the formula to find the tangent plane to…

Q: Let F(x) be a function whose derivative F' (x) = f(x) is graphed below: -3 -2 3 6 --1 = -11.75,…

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Q: What is the slope of the tangent line to the function: f (x) = In (2 x² + 2 x – 11) at the point…

A: To find the slope and equation of the tangent line to the function fx=ln2x2+2x-11 at point P(2,0).

Q: can you show me how I would find the domain of the derivative? What’s the difference between the…

A: We need to find Domain of derivative.

Q: Find an equation of the tangent line to the curve at the given point. xy + x?y? = 12, (3, 1)…

A: Equation of tangent line to the curve: Curve is :                      xy+x2y2=12 at (3,1)…

Q: Using the criterion of the first and second derivatives, find the graph of the function b) F(x) =…

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Q: Match the graph of each function in (a)–(d) with the graphof its derivative in I–IV. Give reasons…

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Q: A car's movement is represented by the function 2x3 + 6x2 + 2x + 3 in kilometers reco at an hourly…

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Q: Implicit differentiation enables us to find dr for any relation involving a and y, even if y cannot…

A: Given cubic equation is                                          y3+y-2x=5 a. It is not possible to…

Q: 3. Find the equation of tangent line of the function f(x) = at the point %3D (6, 4).

A: f(x)=8x-2, at (6,4)Conceptpoint slope form is y-y1=m(x-x1)m is f'(x) at the given point

Q: Sketch the graph of the function f(x) = √x and label the point (4, 2) on the graph. (a) Find the…

A: Function:                      f(x)=x                     Labelling the point= (4, 2) To determine:…

Q: Find an equation of the tangent line to the curve at the given point. xy + x²y? = 56, (7,1) (Express…

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Q: 9, etermine whether the equation y%D - x defines y as a function of x.

A: Yes, because for any input x, the equation yields only one output y.

Q: e equation implicitly defines y as a differentiable function of >

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Q: Find the equation of the tangent plane to the graph of 5y f(x, y) at the point (4, -7). (Use…

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Q: Find an equation of the line tangent to the graph of f(x) = (5x-9)(x + 6) at (2,8). The equation of…

A: F(x) = (5x -9)(x+6)  at point (2,8) here we have to find tangent equation  so tangent slope = slope…

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A: Given that: f(x)=3.cosx2       in (π, 7π)

Q: 13х — 7 - Find the derivative of f(x) = Show all steps. 2х — 1 -

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Q: ax + b (x – 1)(x – 4) at point (2, – 1), determine the values of a and b. If the graph of the…

A: Given: g(x)=y=ax+b(x-1)(x-4) Since, the point (2,-1) is lying on the given curve. So, when x=2,y=-1.…

Q: x2 -4 b) By use derivative sketch the function f(x) %3D 2x

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Q: Derek and Sandy leave an intersection at the same time. Derek travels north at 5 ft/s and Sandy…

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Q: 2. If you will draw the graph of y = x(x+2)², how will you sketch it with respect to the x-axis? A.…

A: Solution..

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A: Given that the curve y=f(x) has a y-intercept of 3.  That means y(0)=3. also given that the tangent…

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A: We will find required equation of  line tangent in the following step.

Q: ind an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Given

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Q: 1. -x² + 6x + 10 -- 12 (x)4 -4- The height of an object shot into the air is given by the equation…

A: The height of an object shot into the air is given as: hx=−112x2+6x+10x is the horizontal distance…

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Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

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Q: Find an equation of the line tangent to the graph of f(x) = 5 – 5x at (3, – 40). The equation of the…

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Q: derivatives in Column B. 1. f(x) = 4 A. f'(x) = 8x 2. f(x) = 4x В. f'(x) = -4x-2 3. f(x) = 4x² С.…

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Q: 04/ Plot the function y 4x- 26x2 + 10x + 8, and its first and second derivatives, for -1sxs3, all in…

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Q: Find an equation of the line tangent to the graph of f(x) = 4 - 6x2 at (4, - 92). The equation of…

A: Here need to find tangent to the graph

Q: Can you please help me step by step with this problem?

A: We can see, that the graph of the function given is a straight line and the slope of the line is…

Q: F(x) = x- 16x3+ 72x2 + 4 (a) Make a sign diagram for the first derivative. f"x) 0 F"(x) > 0 F'(x)…

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Q: A point is moving along the graph of the equation y = −2x2. At what rate is y changing when x = 9…

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Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: Use the definition of the derivative to find the derivative of the function. Show your work by…

A: Follow the steps.

Q: Find the slope and an equation of the tangent line to the graph of the function f at the specified…

A: To determine: The slope and the equation of the tangent line to the graph of the function f at the…

Q: 3.2 The Derivative as a Function ) Usc the Definition, f'=f(xth)- fcx), to find | ん the derivative…

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Q: Find an equation of the line tangent to the graph of f(x) = 3– 7x at (-4,- 109). The equation of the…

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Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A: Solution is given below...

Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A:

Q: Draw a graph to match the description given. f(x) has a positive derivative over (-∞, -1) and…

A: Here, given that the function f(x) has a positive derivative over -∞,-1 & (-1,7) and a negative…