Find f. f ''(x) = 4 + 6x + 36x^2, f(0) = 5, f (1) = 15

Question

Find f. f ''(x) = 4 + 6x + 36x^2, f(0) = 5, f (1) = 15

Answer 1

This is an anti-derivative problem. You need to choose two different letters for your constant of variation (+C and +D perhaps) and then use the two points to solve for C and D.

f '(x) = 4x+3x^2+12x^3+C

f(x) = 2x^2+x^3+3x^4+Cx+D

f(0)=5 --> D = 5

f(1)=15 --> 15=2+1+3+C+5 --> C = 4

f(x) = 2x^2+x^3+3x^4+5x+4