Question

F"(x) = 10 + 6x +36x², f(0) = 5, f(1) = 17

Answer 1

`\displaystyle f'(x)=\int(10+6x+36x^2)\, dx=10x+3x^2+12x^3+c_1\\f(x)=\int( 10x+3x^2+12x^3+c_1)\, dx=5x^2+x^3+3x^4+c_1x+c_2\\\\\\5\cdot0^2+0^3+3\cdot0^4+c_1\cdot 0+c_2=5\\5\cdot 1^2+1^3+3\cdot1^4+c_1\cdot 1+c_2=17\\\\c_2=5\\5+1+3+c_1+c_2=17\\\\c_1=3\\\\\\f(x)=5x^2+x^3+3x^4+3x+5`