3. Use the first derivative test to determine all local minima and maxima for the following function f(x) = 4x³ — 9x² - 30x+6

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A: factor: 3x2-11x-4

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A: NOTE: Refresh your page if you can't see any equations. . for the series the partial sum is  .

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A: Please see the below picture for detailed solution.

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Q: 75. f(x) = (2 - x)ex

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A: We will find the required.

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A: Let's solve given diffential equation.

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A: f(x) = cosπx       , [ 0,2 ] rolles theorm states that if f(x) is continuous in [ a,b }f(x) is…

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A: Given that 3≤f'x≤5 for all values of x. We have to find the bound for f2-f-2.

Q: -6x - 8y y² i+ 4z4 7x+y 2, −4, −1)? Enter an exact answer. et F(x, y, z) = rovide your answer below:…

A: To find the vector associated with (2,-4,-1)

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A: Since you have posted multiple questions, we are supposed to answer only first  question. If you…

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A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

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A: The given curve is:y=7-x ;          1≤x≤7

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A: Let's find value of sqrt(6) by using Newton's method.

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A: 1. Possible   Let set S = {1}  Here, infS = 1 and supS = 1 So, infS= supS  Hence, infS ≥ supS  2.…

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Q: Find the indefinite integral. (Use C for the constant of integration.)         4x3 + 5 (x4 + 5x)2 dx

A: See this solution in below.

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A: The series, ∑n=1∞anp converges iff p&gt;1 and for any a&gt;0

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A: Convert indicated temprature.

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A: (a) limx→0+e4xx

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A: Given, ∫ x2logxdx

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A: The given function fx=cos x-x, 0, 4π. We have to find the relative extremum of the function.