Consider the equation: f(x) = (x2-1)/(x3) a. on which interval is f(x) concave downward? b. on which interval is f(x) concave upward? c. For which values of x does f(x) have a point of inflection?

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

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

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Q: For the function f(x) 5x3 – 8x? + 8x, Step 2 of 2: Find the equation of the tangent line at x = 1

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Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Find the derivative of the function. g(x) = √(4 − 3x2 )

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Q: Find the slope m and the equation of the tangent line to the graph of the function f at the point…

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Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

Q: Use the chain rule to find the derivative of 13 f(x) = 3(6x* – 5a³)* You do not need to expand out…

A: Given that:f(x)=36x4-5x313To find f'(x)

Q: For what values of x does the graph of f(x) = 2x³ – 9x? – 60x – 3 have a horizontal tangent line?…

A: Given,          fx=2x3-9x2-60x-3 have a horizontal tangent line.

Q: Find all values of x such that the slope of the line tangent to the graph of f(x) is 0: f(x) = 3x* +…

A: Given : f(x)= 3x4 +4x3-36x2+6343

Q: Given f (x)=x' -12x +1. Use the second derivative test to determine the local extremum of f (x).

A: Given f(x)= x3 - 12x +1.  To find local extremum of f(x)    If a function has a critical point for…

Q: Find the higher-order derivative. f"(x) = 16x³ – ? 34x f'"'(x) = %D

A: To find the third order derivative , we need to differentiate the gives function with respect to x.

Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Find the derivative of the function f(x) (3x+6)? 6x2+13

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Q: For function, find (a) the equation of the secant line through the points where x has the given…

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Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: Find f'(x) using the rules for finding derivatives 4x2 - 5x + 2 f(x) = 3x +7

A: We have to find

Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: Find f' (x) using the rules for finding derivatives 4x2 – 7x +1 f(x): 2x + 9 f'(x)=O

A: To find The derivative of f(x)

Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: If f(x) = 2x^2 - 10x - 33 , what would the derivative f’(x) be?

A: Given : fx = 2x2-10x-33

Q: Find the higher-order derivative. F'(x) - 7x* - 8x? + 5x f"(x) =

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Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: Find the derivative of f(x)= 5x2 (4+5e")?

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Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

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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: Given f(x) = Vx+ 8, find f' (-4) using the definition of a derivative. %3D Provide your answer…

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Q: Consider the function f(x)=x^2+2x+2  what is the equation of the line of symmetry of f?

A: To find equation of line of symmetry of function fx=x2+2x+2

Q: For the function f(x) = 8x^3-2x^2+2x, Find the equation of the tangent line at x = 2.

A: Please see the answer in Step 2

Q: Given f(x) = 5x² + 5x + 2, find f' (x) using the definition of a derivative.

A: Given function is solved through derivative  detailed solution is given below

Q: Find f'(x) using the rules for finding derivatives 4x2 - 7x +6 f(x) = 2x + 1

A:

Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

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Q: Find the derivative f'(x)=? of the function f(x) = 2x5 +√√x -+ 2x - 3

A: SOLUTION-

Q: Use the second derivative test to find the local extreme values of y= 2x7-x+12

A:

Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: Let f(x) = 3x² – 7x + 5. What is the value of x for which the tangent line to the graph of y = f(x)…

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Q: The derivative of f(x) = x4 + 4e2x is-

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Q: 3x2 – x +1 - Find the derivative f'(x) by hand when f(x) %3D 2x + 7

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Q: Use the definition of the derivative to solve.

A: To determine the derivative of the function.

Q: Use the second derivative test to find the extreme values of the function f(x) = x³ – 3x? – 24x . -

A:

Q: Use the second derivative test to find the extreme values of the function f(x) = 49x + 1. Answer:

A: Second Derivative Test for Local Extrema The second derivative may be used to determine local…

Q: 4. Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Differentiate with respect to x

Q: Given the equation 3x + 2xy -y = 0, evaluate Assume that the equation implicitly defines y as a…

A: We have to find the derivative dydx of the given function.     According to our guidelines, we can…