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: Consider the function g (x) = x³, on the restricted domain [-8, 8]. %3D Where does the derivative…

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Q: Find the derivative of the function. x² + 2 y = 2 – , - 2 -&x(x² + 2, y' = (2² – 2)4

A: Given: The function is, y=x2+2x2-27. The objective is to find the derivative of the function.

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Q: Find the derivatives of the functions in Exercise

A: Given: y=1+x2x34-x-3 To Find: The derivative of the given function

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A: We first expand the expression

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Q: A. Use the definition of derivatives to determine the derivatives of the following functions. 1.…

A: The definition of the derivative of the function fx is f'x=limh→0fx+h-fxh. Substitute x+h for x in…

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Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

Q: Find the derivatives of the functions in Exercise

A: Given function is: ft=t2-1t2+t-2⇒ft=t+1t-1t-1t+2⇒ft=t+1t+2

Q: Find all the higher derivatives of the function f(x) = (2x-5)°. f(x) = f'(x) = p"(x) =|

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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: Find the derivative of the function. g(x) = (2 + (x² + 7)*)3 ow) - 24(3)(2² + 7)*(2 + (x + 7)*)² ×…

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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 derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

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Q: Calculate the derivatives of all orders: F(x), f"(x), F"(x), (4)(x), ..., n)(x),.. x) - ex - 1 "(x)…

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Q: Find the derivatives of the functions in Exercise

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

Q: Find the derivatives with respect to x of the function 2-3x2 A-2x2//2-3x2 -3x /2-3x2 9-2x²/ /2+3x² D…

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Q: х3 — 7 4.) у %3 7 - х' ,3 X y' =

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

Q: Q. 6. Consider f (x) = -* + 2x + 1. x3 3x2 3 Use derivatives to separate the regions where function…

A: If f′(x) > 0, then f is increasing on the interval,and if f′(x) < 0, then f is decreasing on…

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 of the functions in Exercise

A: Find the derivatives of the functions in Exercise

Q: Find the derivative of the following functions: y=-3x^3-2+3^√1-x -1/√2x

A: To Determine: find the derivative of the function  Given: we have y=-3x3-2+31-x-12x Explanation: we…

Q: Graph the first and second derivatives of the given function: f(x)= x3+ 2 x2 - 3x

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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}

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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: Find the derivatives of the functions y = 20(3x - 4)1/4(3x - 4)-1/5

A: Given: y=20(3x−4)14(3x−4)−15

Q: Let g be a function with derivative given by x2 - 2x - 8 g'(x) = V2x³ +5 - 1<x <5 %3D . At which…

A: Occours

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: 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 first and the second derivatives of the function. y%3D 6-x

A: The given function is: y=x6-x  =-xx-6  =-x-6+6x-6  =-1+6x-6  =-1-6x-6

Q: Calculate the derivative of the function. g(x) = (x² – 3x – 1)-7 %3D g'(x) =

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

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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: Find the first 3 derivatives of f(x)=-5x^-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: Find the equation of the tangent line to the graph of the function at the indicated coordinates. 1.…

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Q: Let f be a function with first derivative given by f' (x) = (x + 1)(x – 2)(x – 3). At what values of…

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Q: Find the derivatives of the functions y = (2x - 5)-1(x2 - 5x)6

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

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Q: Find the derivatives of the functions w = (2x - 7)-1(x + 5)

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Q: Find the derivatives of the functions . 1. y = x5 - 0.125x2 + 0.25x 3. y = x3 - 3(x2 + p2) 5. y = (x…

A: Given,

Q: Compute the derivative function f'(x) algebraically. f(x) =x²-9 O a. f'(x)= 2x O b. f'(x)=2 O c.…

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Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 A) - = 2(x+ 1)(x2 + 1)-4(2x2 - 3x - 1) B) Y =-2(x +…

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