How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show at least two periods and clearly lable the x-intercepts.

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) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: Given, f(x)=sin 2x ln x2; (1,0)

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

A: Solution:

Q: (a) Find the equation of the tangent line to the graph of the function f(x) = 3x² at the point (-2,…

A: (a)   Differentiate the function with respect to x is,   Substitute -2 for x in the above equation.

Q: Find an equation for the tangent line to the graph of the given function at (3,2). f(x) = x² - 7…

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Q: Disprove the statement ln x / ln y = ln x - ln y,  by, a) Letting y equal a positive constant of…

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Q: Find an equation for the tangent line to the graph of the given function at (-3,1). f(x) = x² – 8…

A: Given: The function fx=x2-8and the point -3,1. To find: The equation of tangent line to the graph of…

Q: Question 1 ( Use the First Derivative Test to find the local maximum and minimum values of the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: (а) (b)

A: To plot the graph for f’(x) and f” (x) consider the graphical meaning for f’(x) and f” (x) for the…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: Solve using implicit differentiation.    y cos x = x2 - y2

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Q: Determine the point(s) at which the graph of f(x) =  -4x/square root of 2x-1   has a horizontal…

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Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Find any relative extremes of the functions and use a graphing utility to confirm your results. f(x)…

A: Given: f(x)=xcoshx-1-sinhx-1 Concept: Critical Point:x=c is called critical point of f(x) if…

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

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Q: shows the graphs of the first and second derivatives of a function y = ƒ(x). Copy the picture and…

A: The graph of y=f"(x) is a linear function. So it is of degree 1.  The graph of y=f'(x) is a…

Q: 3x-4 1. Y= Arctan 4

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Q: 1. If the first derivative is zero and the second derivative is positive, what can be concluded in…

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Q: Using the first and second derivatives, sketch a graph for y=Sin^2x+1.

A: Explanation of the solution is given below....

Q: 3 + 3x – 5 Find the local maximum by solving the derivative P'(x)=0, – 2x + -- %3D |

A: Given Find out local maximum

Q: Find the derivative of the function. y = (tan-1(8x))2

A: Function y=(tan-1(8x)2 To find the derivative of the given function.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Use the basic definition of Cosh to find the derivative of the function, Coshx=ex+e-x2. Find the…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given, y=coshtan-13x

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A:

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

A: Since, you have ask multiple part's in the question. I am answering for first three parts. Please…

Q: Given to the right is the graph of the function f(x) =(x² +2)" (dark graph) and its second…

A: Given, fx=x2+2-1 The graph of f(x) and f''(x) is shown as: The equation of a line in point-slope…

Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

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: Find an equation of the tangent line to the graph of the function at the given point.…

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Q: Find the equation of the tangent line to the graph at the indicated point. f(x)=x^2-1 ; x=8

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Q: Draw simple graphs of the first and second derivatives of the function y = f(x) whose graph is given…

A: Given,

Q: Find an equation for the tangent line to the graph of the given function at (-5,29). f(x)=x² +4 Find…

A: f(x)=x^2+4   (-5,29) slope=m=dy/dx m=dy/dx=d(x^2+4)dx=2x m=2x (-5,29) m=2(-5)=-10

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

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Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given f(x)=sinx4         , 0, 8π

Q: The graph of the first derivative of a function is shown a) How can we know in which intervals the…

A: Here we have the graph of the first derivative of a function is shown.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given: y=sinh(3x2 ln(1+3x)) Use chain rule for derivative: ddx(f(g(x))=f'(x)ddxg(x) And uv rule for…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) =…

A: Given: fx=x+2x-22=y To find the slope of tangent line at point (6,4) ,we need to find the value of…

Q: Find the equation of the tangent line to the graph of the function f(x)= 2+5 z-8 at the point

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Q: Find y" by implicit differentiation.   x3 + y3 =1

A: We find y' first

Q: Find the function whose tangent has slope xln√x for each value of x>0 and whose graph passes through…

A: It is given that the slope of the tangent is equal to dydx. This question can be solved using the…

Q: On the interval -2<x<-1/2, the graph of the curve f (x) = 2x° +3x2 - 12x - 7 is: %3D Support answer…

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Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given- fx=sinx4,0,8...........(1) As we know that inflection point is a point on the graph at which…

Q: How is the graph of y = Sin(x - 30) different from that of the function y = sin x?

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Q: The function g has first derivative given by g'(x) What is 1+x + x3 the x-coordinate of the…

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Q: Find f′(x) and find the equation of the line tangent to the graph of f at x=2.   f(x)=3x/2^x

A: Given:fx=3x2x , x=2Equation of Tangent line:y-y1=mx-x1ddxuv=vdudx-udvdxv2

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: I found the derivative of f(x), I put  f'(x) equal to zero and obtained cosx=-1/2. What is the next…

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Q: 24. Consider the graph of y = Use limits and 1+ eax first derivatives to determine how the shape of…

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Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…