Question

Encontre f tal que: f" (x) = 3x+2

Answer 1

$\displaystyle\sf\int\dfrac{d^2}{dx^2}=\dfrac{d}{dx}\\\displaystyle\sf \dfrac{d}{dx}=\int (3x+2)=\dfrac{3}{2}x^2+2x+k\\\displaystyle\sf\int\dfrac{d}{dx}=f(x)+k\\\displaystyle\sf f(x)=\int\bigg(\dfrac{3}{2}x^2+2x\bigg)=\dfrac{1}{2}x^3+x^2+k$

$\large\boxed{\boxed{\boxed{\boxed{\sf f(x)=\dfrac{1}{2}x^3+x^2+k}}}}\blue{\checkmark}$