1. Match the equation of the following functions to the appropriate graph. Justify your answer. . .. siication) f(x) = (2)2(x-3) + 2 h(x) = - () 2x+2 - 2 Justify: Justify:

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x= 2. X-6 f(x) = 5x - 1

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Q: 7/8 For what value of x does the graph of f(x) = x8e* have a horizontal tangent?

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Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

A:

Q: Given that the graph of f(x) passes through the point (9, 6), and that the slope of tangent line to…

A: First calculate f(x) then use (9,6) to find the constant in f(x). Then find f(5).

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: Find the domain of function defined as follows. y = ln(x2 - 16)

A: y=lnx2-16Domain:       The domain of a function is the set of all possibleinputs for the function

Q: The graph of f (x) = |x| is reflected over the x-axis, shifted vertically up 1 unit, horizontally 3…

A: Given that fx=x is reflected over the x-axis shifted vertically up 1 unit ,horizontally compressed…

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

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Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

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Q: Show analytically (that is, without reference to a graph) that h(x) = v1 + x is always increasing,…

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Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Finding the g'(4) from the given conditions.

Q: If n is positive and even, where is the graph of f(x) = xn increasing and where is it decreasing?

A: For f(x)= xn  where n is positive and even. for these type of function the general graph is given…

Q: a. What are the net total savings during the first year of use of the​ machine? b. What are the net…

A:

Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Determine the equation of the line tangent to the graph of the following function at x = 0. g(x)…

A: The given function is

Q: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = Inx?;…

A:

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: (b) Write the equation of the line tangent to the graph of f(x) at z 1, and graph it below f(x) =…

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

A: To select: The correct options. Given: The function is g(x)=x3-4x+1 and the line tangent to the…

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: For what values of x does the graph of f(x) = x3 + 3x 2 + x + 3 have a horizontal tangent?

A: the given function is: fx=x3+3x2+x+3 we have to determine for what values of x does the graph of…

Q: For what value(s) of x does the graph of f(x) = 4x3 - 6x2 - 144x - 24, have a horizontal tangent?

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Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

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Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A:

Q: Find all the values of x where the graph of f(x) = 2x – 24x2 + 72 - 1 has a horizontal tangent line.…

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Q: given that the graph of f(x) passes through the point (10,9) and the slope of its tangent line…

A:

Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: If f is a one-to-one function with f(3) = 5 and f'(3) = 2, find the equation of the line tangent to…

A: To find tangent line.

Q: If f (x)= x2 - 4x, at which point on the graph f (x) is the tangent line horizontal

A: topic - slope of tangent line

Q: Find the slope of the line tangent to the graph of f(x) = -1₂ at x = 3. x+2 Provide your answer…

A:

Q: 6. a. Use an x- interval of 0.0001 to determine the instantaneous range of change of the function…

A: Consider the given function. fx=x4+8x3+19x2+12x The objective of the problem is to find the…

Q: 1. Use the second derivative test to find the relative extrema of the following function. f (x) =…

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Q: A researcher believes that if x thousand individuals among a susceptible population are inoculated…

A: Given: I(x)=aRx-b R=0.9

Q: 8. Given the function f(x)%=2x3 -5x3 , find the point where the tangent is horizontal to the curve.

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Q: Find the equation of the line tangent to the graph of f(x) = 3 - 2x at x = 3. Provide your answer…

A: The given curve is fx=3-2x and point is x=3 The slope of tangent on a curve f(x) at x=a is given by,…

Q: Given the graph of f(x) below, for what value(s) of x is f(x) non-differentiable?

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Q: Find the slope of the line tangent to the graph of the function at the given value of x. y = x4 + 2x…

A: Given : y = x4+2x3+2x-2

Q: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line…

A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the…

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 5. Find the length of the curve given by the graph of the function f(x) = x/x, for a in [1,4].…

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Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: The population of the United States can be modeled by the function p(x) = 80.21e131x where x is the…

A: We have to graph P(x) and predict population in given years.   According to our guidelines we can…