Find f if f''(x) = 4 - 18x, f(0) = 7, f(2) = 5?

Answer 1

f'(x) = 4x - 9x² + C and f(x)= 2x² -3 x³ +Cx +D using f(0)= 7 and f(2)= 5 gives the following f(0)= 7 =D

and f(2)= 5 = 2•4 -3• 8 +2C + 7 solving for C gives 2C = 5+ 24 -8 -7 or 2C= 14 and C= 7 Therefore

f(x) = 2x² -3x³ + 7x +7.