Find f. f ''(x) = x^−2, x > 0, f(1) = 0, f(6) = 0

Question

Find f. f ''(x) = x^−2, x > 0, f(1) = 0, f(6) = 0

Answer 1

f"(x) = x^-2 = 1/x^2

f'(x) =-x^-1 + c or -1/x +c

f(x) = -lnx +cx + k

f(1) = 0 = 0+0+k = k

f(x) =-lnx +cx

f(6) =0 = ln6 +6c

6c = -ln6

c = -ln6/6 = about 1.792/6 = 0.299

f(x) = -lnx -(ln6)/6)x or about -lnx-.3x