Question #020d3

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Answer 1 · 2017-03-20T20:44:41

#y = 10 sqrt(x) + 3#

In math-speak you have:

#y' = alpha/sqrtx# where #alpha# is some constant

Compared to your other stuff, This is simple power rule material:

#int x^n dx = (x^(n+1))/(n+1) + C#

It solves as:

#y = 2 alpha sqrt(x) + beta#

#3 = 0 + beta implies beta = 3#

#23 = 2 alpha cdot (pm 2) + 3 implies alpha = pm 5#

#implies y = pm 10 sqrt(x) + 3#

But it has to go through #(4,23)# so it is:

#implies y = 10 sqrt(x) + 3#