Answer:
y = x³ - 4x² + 27
Step-by-step explanation:
given [tex]\frac{dy}{dx}[/tex] = 3x² - 8x , then
y = ∫(3x² - 8x) dx
integrate each term using the power rule
∫(a[tex]x^{n}[/tex]) = [tex]\frac{a}{n+1}[/tex] [tex]x^{n+1}[/tex] : n ≠ - 1
y = x³ - 4x² + c ( c is the constant of integration )
to find c substitute (- 2, 3) into the equation
3 = (- 2)³ - 4(- 2)² + c = - 8 - 16 + c ⇒ c = 27
y = x³ - 4x² + 27
