Sketch the graph of a twice-differentiable function y = f(x) that passes through the points (-3, -2), (-2,0), (0, 1), (1, 2), and (2, 3) and whose first two derivatives have the following sign patterns. -3

Q: Find the derivatives of the functions g(x) = x2 - 4/x + 0.5

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Q: Assume that f (1) = 4, f' (1) = -3, g(2) = 1, g' (2) = 3  Calculate the derivatives of the following…

A: Given, f1=4,f'1=-3g2=1,g'2=3

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A: Given:        y= x+12x2+1-3

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Q: if f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1, then the derivative of f(x).g(x) evaluated at x =…

A: Given: f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1

Q: Assume that f(1) = 4, f'(1) = -3, g(2) = 1, g'(2) = 3 Calculate the derivatives of the following…

A: Given that f1=4,  f'1=-3,  g2=1  and  g'2=3. (a) Compute the derivative of fgx at x=2 as follows.…

Q: Find the derivatives of f(x)=(ax4+b)6   and   f(x)=axe-bx+15 Assume that a and b are constants.

A: Given query is to find the derivative of the expression.

Q: Let (x0, yo) = (2,6) and (x1, Y1) = (2.5, 6.2). Use the following graph of the function f to find…

A: Given that, The points of passing of function f are following, (x0, y0) = (2, 6)   and     (x1, y1)…

Q: Calculate the derivatives of all orders: f'(x), f"(x), f''(x), f(4)(x), ..., f(n)(x), .. .. f(x) =…

A: f(x) = e5x

Q: Calculate the derivatives of all orders: f"(x), f"(x), f"'(x), f(4)(x), ..., f(n)(x), . .. f(x) =…

A: Given function:    f(x) = (-4x+1)3  we have to calculate the derivatives of all orders.

Q: Find the derivatives of the functions in Exercise

A: y=x+1x+2x-1x-2

Q: Find the derivatives of the functions y = 1/xsin-5 x - x/3cos3 x

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Q: х3 — 7 4.) у %3 7 - х' ,3 X y' =

A: Given function, y=x3-77-x3

Q: 12) Select an appropriate graph of a twice-differentiable function y f(x) that passes through the…

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Q: 1. Find the derivative of each function a. f(x) = -3x* + 2x² + 5 b. f(x) = 2Vx - 3 %3D c. f(x) =…

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Q: Find the derivatives of all orders of the functions y = (x - 1)(x + 2)(x + 3)

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Q: Find the derivatives for each function. 1) y=e^(2x+x^(2))  2) y=2xe^(x^(2)) 3) y=ln((x+1)(2x+1))…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Let (x0,y0)=(2,6) and (x1,y1)= (2.5,6.2). Use the following graph of the function f to find the…

A: We first find the slope of f(x) at x=2 using the given tangent. Slope=f'(2)= slope between (2,6) and…

Q: A) Find the domain and range (for TWO only) 1) y = V9 - V9x 2) y = V4 – x² 3) y= у 3 B/ Draw the…

A: given is 1) y=9-9x    y=9-3xdomain =x∈R : 0≤x≤9range ={y∈R : 0≤y≤3}

Q: Compute the derivative function f' (x) algebraically. f (x) = –x² – 2x O f' (x) = 2x – 2 O f' (x) =…

A: Derivative of xn= nxn-1

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Q: Find the derivatives of the functions y =(x + 1)(x + 2)/(x - 1)(x - 2)

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Q: Find the derivatives of the functions in Exercises y = (x + 1)2(x2 + 2x)            6. y = (2x -…

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

Q: (A) Find the derivative of y with respect to x of (x+1)5 1. у%3D (x+2)20 2. y = (x2 + 1)-2(x* + 1)3…

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Q: Calculate the derivative of the function. g(x) = (4a? + 2x +2)* O g' (x) = (-16æ² + 8x + 8) O 9' (x)…

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Q: Assume that functions f and g are differentiable with f(-3)= -5, f(- 3) = -4, g(-3)=2, and…

A: Equation of a line

Q: Let (x0,y0)=(2,6) and (x1,y1)= (2.5,6.2). Use the following graph of the function f to find the…

A: Given points that lie on tangent are:

Q: Evaluate the derivatives of the given function for the given value of x.  y = (x^2-3x+3)…

A: y = (x² - 3x + 3)(5 - 5x - 2x²) So, y' = (2x - 3)(5 - 5x - 2x²) + (x² - 3x + 3)(- 5 - 4x)

Q: Find the derivative of the function. (x² + 1)6*². 1 u(x) = u'(x) =

A: This question is related to differentiation solve in step 2.

Q: Let (x0, Yo) = (3, 6) and (¤1, y1) = (3.2, 6.1). Use the following graph of the function † to hnd…

A: Definition used -                    Derivative at a point = slope of the tangent line passing…

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: here x-intercepts are x=-3 and x=1 so the factored form of the parabola is…

Q: Find the derivative of the function h(x)=g(f(x)) at the point x=1 if f(1)=2, f(2)=0, f'(1)=-4,…

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Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative

Q: Assume that functions f and g are differentiable with f(- 3) = – 5, f'(- 3) = – 5, g(-3) = 4, and…

A: Given F(x)=f(x)g(x)

Q: Find all the higher derivatives of the function f(x) = (4x-5)°. P (x) =] f"(x) = f"(x)=

A: Differentiate above function with respect to x

Q: A function, f, and its derivative are given below. Which of the following is an equation of the…

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Q: Find the derivative of the function at the given point in the direction f(x,у) %3D - 5х - 2у,…

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Q: Consider the function g (x) = x3, on the restricted domain [-8, 8]. Which of the following is the…

A: Explained below

Q: . Find the derivatives of the following function (a) y-²-3+2 (b) y=-2+

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Q: A graph of y= f(1) is shown. In the same coordinate system, sketch a graph of the derivative…

A: The given graph is of a parabola with the vertex (0,-1). So, its equation is:…

Q: FIND THE DERIVATIVE OF THE FUNCTION DESCRIBED. (25 1. y (x2- 1) (2x+1) 2. y 2x2 (4x² + 3x- 5) 3 y +1…

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Q: Compute the derivative function f' (x) algebraically. f (x) = -x? – 2x O f' (x) = -2 – 2 %3D O f'…

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Q: Find the equation of the tangent line to the graph of the function at the indicated coordinates. 1.…

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Q: A function, f (x), has derivatives: f'(x) = x² (x – 3) f"(x) = 3x(x – 2) Which of the following…

A: Consider the derivatives of the function fx f'x=x2x-3f''x=3xx-2 First, find the original function…

Q: Sketch the graph of a twice-differentiable function y = f(x) that passes through the points (-2, 2),…

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Q: Sketch a possible graph of y = f(x), using the given information about the derivatives y′ = f ′(x)…

A: From the given problem, we need to draw graph as per given properties of graph.We must need to…

Q: 4. Find the derivatives of the following functions. a. y= 2x b. y = x³ C. y= 4x -7

A: a. y=2x Differentiating both side with respect to x dydx=2b.y=x3Differentiating both side with…