madas9nth0agonzan madas9nth0agonzan

26-11-2016
Mathematics

Answered

Find f.

f'(x)=(sqrt(x))(6+10x)

f(1)=11

Verified Answer :

alsteva alsteva

30-11-2016

It is a matter of integrating f′:

\(f(x)=\int \sqrt{x}(6+10x)dx, \\ \\f(x)=\int 6x^{1/2}dx+\int10x^{3/2}dx, \\ \\f(x)=4x^{3/2}(x+1)+C.\)

Combine the constants. Then use the initial condition to find C:

\(11=8+C\implies C=3\)

Therefore,

\(f(x)=4x^{3/2}(x+1)+3.\)

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