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Question 1 f is a function whose domain is (0,∞) and whose first derivative is f '...

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Basic Math

Question 1

f is a function whose domain is (0,∞) and whose firstderivative is f ' (x) = (4 − x)x -3 for x >0

a) Find the critical number(s) of f. Does f have a localminimum, a local maximum, or neither at its critical number(s)?Explain.

b) On which interval(s) if f concave up, concavedown?

c) At which value(s) of x does f have a point ofinflection, if any?

Question 2

A rectangular box with a square base has a surface areaof 150 cm2 , obtained by adding the areas all six sidesof the box. Find the dimensions of the box with the largestpossible volume.​​​​​​​

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