Use Descartes's Rule of Signs to dete 17) f(x) = 3x -5x4 + x + 10

Q: d the second derivative of the functi =) = [3x° +6}* a. f" = 90x*(6+3x)ʻ(24+90x°) b. f" = 90x*(6…

A: We have to choose the correct answer from the given options according to the given information

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

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Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: What is the derivative of 2.x + 3 f (x) = 2x2 + 7x + 6

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Q: True or False: A canceling linear factor in the numerator and denominator, when set equal to zero,…

A: If there is a hole in a graph of a function than there must be common factor in numerator and…

Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: -x²+5 < f (x) < x+1 2

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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: 2 - ) at x = 4 1+ x)

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Q: Use the chain rule to find the derivative of f(x) = 4(8z³ – 32")² You do not need to expand out your…

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Q: Find the critical points and apply the Second Derivative Test (or state that it fails):  f (x) = 3x4…

A: fx=3x4-8x3+6x2 Differentiating with respect to x, we get f'x=3·4x3-8·3x2+6·2x=12x3-24x2+12x Again…

Q: Find the extreme values on the interval:  f (x) = ex − 20x − 1, [0, 5]

A: Given, fx=ex-20x-1 in [0,5]

Q: What is the minimum number of times you would expect f(x) 6 in the interval (0, 40? %3D

A: from the given table we cansay (As f(x) in continuoun everywhere)∃ x1∈ (0,10) such that,…

Q: Let Ax) = 8x_+ 3x² – x + 1_. a. Determine f (x). b. Use 13a to find the equation of the tangent line…

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=7−67xf(x)=7-67x, and the line…

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Q: зах (х+2)/x2+4x+3

A: Please refer the attached image for complete solution. THANK YOU.

Q: 3x² (9 – x² ) 2 2 (9 — 3х2)

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Q: 4) Find the derivative of f(x) = (5x² - 3)² in two different ways.

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Q: Find the critical points and apply the Second Derivative Test (or state that it fails): f (x) = x4 −…

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Q: y = 2x' + 5x from the point (-2,-26) to the point (4,148), you'd have to compute f(x)dx

A: Given: y=2x3 +5x Point (-2,26) ,(4,148)

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: What is the difference between the maximum and minimum of the quantity (x2y2)/25 where x and y are…

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Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

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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: (2022) , find feua (0) (1-x3 2x given f(x) 2

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Q: in of (fo f)(x). (Enter your answer using

A: We have to find the following conditions according to the given information

Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

Q: Find the extrema of f(x) = 3x4 − 4x3 on the interval [−1, 2].

A: The given function f(x) = 3x4 − 4x3 on the interval [−1, 2].

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: (1, if x 2

A: Using the given piece wise function, we can plot it in given intervals.

Q: What is the derivative of 6x/((x^3)+3)^2? I think I need to factor out an ((x^3)+3) from the…

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: the first dirivative of f(x) =( 5x4 - 6x)-3 will be _______

A: Given : f(x) = (5x4 - 6x)–3

Q: The higher derivative of y = 5x³ – 2x is O 15x2 – 2 О 30 O 30x

A:

Q: find the critical points and apply the Second Derivative Test (or state that it fails). f(x) = x^2 −…

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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 critical points and apply the Second Derivative Test (or state that it fails).…

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Q: 2) Use the second derivative test to find the local extreme values of y= x5 – 5x³+7

A: Given that, We will find the local extreme values of the function as following.

Q: Find the extreme values of on [-2,2]. f(x) = ret, x < 0 2x³9x² - 12x, x ≥ 0

A: Solution of given question is written in below steps.

Q: Find all local extrema of f (x) = 4x3 – 3x² – 6x + 7 - -

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Q: Find the equation of the line tangent to f(x) = 4x³ + 9x – 7 when x=3. O f(x) = 135x - 288 o f(x) =…

A: Given, f(x)=4x3+9x-7 and x=3 The equation of a line in point-slope form is given by y-y1=mx-x1…

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: Show that |x + y|≥||x|−|y||, solution without using piecewise function

A: Just I have used the triangle inequality of absolute function and easily prove that the given…

Q: What is the first derivative of p(æ) = In (4x3 + x² +1)?

A: Given function is p(x)=ln4x3+x2+1

Q: The derivative of f(x) = 10 (x2 + 13z) is О 10х + 130 О 10х ?(2т + 13) O 10 O -10x 3(2x + 13) O -…

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Q: 3) Find the derivative of f (x) = Vx3 – 4x²

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Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Find the derivative off(x) = 5(7x3−2x+ 1)−3.

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Q: What are the critical numbers of the function f(x)= 2x^(3)-2x^(2)-16x+1?

A: Let's find.