Find f by solving the initial-value problem. (Remember to use absolute values where appropriate.)

Question

f'(x)= x+7/x. ; f(1)=8

Answer 1

f'(x) = x + 7/x

f(x) = x^2/2 +7lnx +c

f(1) = 8 = 1/2 +c

c = 8-1/2 = 7.5

f(x) = (1/2)x^2 + 7lnx + 7.5

ni absolute value symbol on my keyboard but lnx requires x>0