The following five points lie on a function (1,20) , (2,4), (5,3), (6,2), (10,1)

Question

The following five points lie on a function (1,20) , (2,4), (5,3), (6,2), (10,1) . FIND AN EQUATION THAT PASSES THROUGH THESE POINTS AND HAS THE FOLLOWING FEATURES: -There are three inflection points -There is at least one local maximum -There is at least one local minimum -At least one critical point is not at a given point -The curve is continuous and differentiable throughout -The equation is not a single polynomial, but must be a piesewise defined function There are many possibilities that meet this criteria. Prove that your answer function does so. Please solve in terms of the AB CALCULUS course !!!

Explanation / Answer

y = x5+ax4+bx3+cx2+dx+e

CONDITIONS:

a. 1+a+b+c+d+e = 20 => a+b+c+d+e = 19

b. 32+16a+8b+4c+2d+e= 4 =>16a+8b+4c+2d+e= -28

c. 3125 + 625a +125 b+ 25c+ 5d +e = 3

d. 7776 + 1296 a + 216b + 36c+ 6d +e = 2

solve to get the answer.

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