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  1. mathematics
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  3. a) let f(x) = ?x^4 ? 4x^3 . (i) find the intervals

a) Let f(x) = ?x^4 ? 4x^3 . (i) Find the intervals of increase/decrease of f....

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Basic Math

a) Let f(x) = ?x^4 ? 4x^3 . (i) Find the intervals ofincrease/decrease of f. (ii) Find the local extrema of f (valuesand locations). (iii) Determine the intervals of concavity. (iv)Find the location of the inflection points of f. (v) Sketch thegraph of f. (You can choose your own scale for the graph)

b) A farmer wants to fence in an area of 6 km2 in a rectangularfield and then divide it in half with a fence parallel to one ofthe sides of the rectangle. Find the dimensions of the rectangularfield that minimize the amount of fence used.

Express the area of the region bounded by the graph of f(x) = 2+ ? x and the x-axis in the interval [3, 8] as a limit of sumsusing right endpoints. Do not evaluate the limit.

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