The function f graphed here consists of two straight line segments and two quarter circles. Find A(6) and A'(3)

Q: use the definition of derivative to find f prime (x). f(x)= 3(2x-1)^3

A: Given function is fx=32x-13. To find the derivative of the function using definition of derivative.…

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2…

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Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: USE THE SECOND DERIVATIVE TEST To FIND LOCAL EXTREMA OF THE FUNCTION. F(x)= -x³ +12x² -5ON R.

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Q: Find the derivative of the function f(x) = -8x² – 18x + 23 by definition of derivatives f(x + h) –…

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Q: Find the points of inflection given the function: Given the function f(x) = 2x³+ 3x²-12x-9 Where…

A: For the inflection point, second derivative is equal to zero.

Q: Sketch the graph of the function f(x)=-x2 +4x-1. Find the equation of the line that is tangent to…

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Q: Use the guidelines from section 4.5 to graph the function f(x) = x2/3 (6 – x)/3 For your…

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Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3(x -…

A: Given that a function f(x) and we find local extrema. For local extrema we do first derivative of…

Q: Find the equation of the line tangent to the graph of the function at the indicated point. 5) f(x) =…

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Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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Q: The function f has a continuous second derivative, and it satisfies f(-8) = 5,f'(-8) = 0 and f"(-8)…

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Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Given: The  slope of  a curve:   To determine: The equation of the curve f(x)

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

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Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: Find the points where the graph of the function has horizontal tangents. f(x) = 3x^2 + 7x - 5

A: We have to find the points where the graph of the function has horizontal tangents.…

Q: Find the equation of the tangent line to the graph of the function f (x) = (x2 +8) (x - 3) at the…

A: Given : f(x) = (x² + 8)(x - 3) at the point      (1, -18)

Q: Using the second derivative criterion, find the graphs of the functions a) F(x) = x*– 8x² +3

A: Given- (a)  Fx=x4-8x2+3 To Find- The graph of the above functions using second derivative.

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Use the Second Derivative Test to find all relative extrema of the function f(x) = 2x - 6x +7.

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Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Find the derivative of the funchion f(x)=9x-5

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Q: Find the slope m of the line tangent to the graph of the function f(x) = 5 - 6x at point (-1, 11)

A: Given:  f(x)=5-6x                y=5-6xDidderentating y=5-6x   with respect to 'x'  and substituting…

Q: Sketch the graph of the derivative for function shown.

A: Plot the derivative for -∞<x<0. The function f(x) is constant in the interval -∞<x<0 so…

Q: A) function is defined by f(x) = {²1₂ ² if x20 if x<0 Evaluate f(0), f(1)and f(2) and sketch the…

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Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given: f'(x)=-2x8-x2,    2,7 Integrate the given function to obtain the function f(x). The formula…

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: Compute the Indicated derivative. 7. f" (x) for f(x) = 5x2-14x + %3D

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Find the extreme values of the function f on the interval [3,4]. (x^4)+(4/x)

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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) = 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 that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Using integration.

Q: Consider function y = 4x divided by x2 + 3 Determine all relative and absolute maxima and minima…

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Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Find a function f(r) with a derivative given by f'(x) = 6x2 + 4x – 5 and f(1) = 4. %3D

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Q: Evaluate the second derivative of the function at the given point f(x)=9/√x+9    (0,3)

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Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

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Q: Find the derivative of the function f(x) = (2x² + 5æ + 2)° at æ : - 2)* - 1 f'( – 1) = 3

A: Given :f(x) = (2x2+5x+2)3 at x = -1First we will find the derivative of the f(x)

Q: The function f(x) = 2x³ – 27x² + 108x + 9 has derivative f'(x) = 6x² – 54x + 108. f(x) has one local…

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Q: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get