Given f (x) = sin (z) and g (x) = x, the graph of the combined function h (x) = f (x) g (x) most likely resembles: O a) 2- -2n -3n/2 n/2 3ry2 2n -2- -

Q: Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: On the interval –5 < x < 6, for how many values does f (x)(graphed below) have a derivative equal to…

A: Given:

Q: A curve, y=f(x) passes through the point (1, −1)(1, −1) and the slope of the tangent at any x is…

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Q: The derivative of the function f is defined by f' (x) = (x² + 4) cos (x - 3). If f(6) = -1, then use…

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Q: The derivative of the function f is defined by - f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what…

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Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: The range of F (x) = 3 sin 2 x is -3≤F(x)≤3 -1≤F(x)≤1 -2≤F(x)≤2

A: The given function is: F(x)=3 sin(2x)

Q: -4 Find the line 1. f(x) = x³ - 2. f(x) = cos 2 3. f(x)

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Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: (1 point) Suppose f" (x) = –16 sin(4æ) and f' (0) = –4, and f(0) = -1. -1. f(T/2) :

A: Given,f''x = -16sin4xIntegrating on both side with respect to x, we get;f'x = - 64cos4x +…

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the vertical and horizontal asymptotes of f(x) = cos x +4Vx

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

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Q: 1 Sketch a graph of the function f(x) = 3 sin 5- 4- -87T -7 -6I -5 -47T -37 -27 27T 37T 47T -2- -3…

A: the amplitude of the function is 3 the time period of the function is  2π1/4=8π

Q: Given the function g(x) = 4x° + 6x² – 24x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 5) cos (3x). What is the x-coordinate…

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

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Q: Given the function f(x)=x4-6x2-60x2+134x+30 The value x=1 satisfies the equation f'(x)=0 (that is,…

A: The function f(x) is maximum when f''(x)&lt;0 at x=a The function f(x) is minimum when f''(x)&gt;0…

Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: If f and g are the functions whose graphs are shown, let  u(x) = f(g(x)),   v(x) = g(f(x)), and…

A: The given graphs of f and g are

Q: Given the function g(x) = 4x° + 30x2 + 48x, find the first derivative, g'(x). gʻ(x) = Notice that…

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Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: If f (x) = sin 2x , find all of the stationary points of f (x) on 0<x<2n

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Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

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Q: Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x)= Notice that…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: The derivative of the function f is defined by f'(x) = x? – 5x + 5 cos (3x? – 3x). If ƒ(-2) = –4,…

A: Given: f'x = gx = x2-5x+5cos3x2-3xf-2 = 4------------------------------Aim: To find absolute maximum…

Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: Given the function g(x) = 8x° + 84x² + 288x, find the first derivative, g’(x). = (x),6 Notice that…

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Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: 2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) =…

A: We can find the answers as below.

Q: The function f(x) = (6x + 9)e-6z has one critical number. Find it.

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Q: On the graph of f(x)=sinx and the interval [2π,4π), for what value of x does the graph cross the…

A: On the graph of f(x)=sinx and the interval [2π,4π), for what value of x does the graph cross the…

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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