Find a and b such that y=asrtx+ b/srtx has (1,8) as a point of inflection.
2 answers
Find a and b such that y=a sqrt x + b/sqrtx has (1,8) as a point of inflection.
y = a√x + b/√x
y' = a/2√x - b ÷ 2x^3/2 = (ax-b) ÷ 2x^3/2
y'' = (3b-ax) ÷ 4x^5/2
so, y''=0 when x = 3b/a
3b/a = 1 ==> a = 3b
y(1) = 3b + b = 4b = 8 ==> b=2, so a=6
y = 6√x + 2/√x
y' = a/2√x - b ÷ 2x^3/2 = (ax-b) ÷ 2x^3/2
y'' = (3b-ax) ÷ 4x^5/2
so, y''=0 when x = 3b/a
3b/a = 1 ==> a = 3b
y(1) = 3b + b = 4b = 8 ==> b=2, so a=6
y = 6√x + 2/√x