Consider the function f(x) 2x + 6x2 18x 54. a. Find the first derivative. f'(x) b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease.

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A: integration by substitution method 

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A: Topic:- derivatives and equation of line 

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A: This question can be solved using integration by substitution.

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A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

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A: topic - mean value theorem

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A: To find the second derivative.

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A: This question is based on application of derivative.

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A: We have to find first 5 term of Given sequence.

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A: topic - indefinite integral

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A: Let's find. 

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Q: 9. Evaluate the definite integrals (give exact answers): a) (2x + 3)(r – 5)dx b) e -(1³ – 2x² + 1)dx

A: I am attaching image so that you understand each and every step.

Q: Q4) Find the Asymptotes of the following functions: x³ – 4x² - 1) y x² – 2 x² – 4 2) f(x) : %3D x² –...

A: Solution is given below

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A: Given data:

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A: topic - derivative of a function

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A: Given secA+tanA=x To find secA:

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A: maximize the function

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A: Note: According to our answering guidelines we have to answer only one question if multiple are post...

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A: This is a problem of series and sum calculator. By using integral test we will identify the nature o...

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A: We have to find F(x) by indefinite integral

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