Question

Please help!!!!! And show all working out!!!

Answer 1

y = x³ - 4x² + 27

Explanation:

given
`(dy)/(dx)` = 3x² - 8x , then

y = ∫(3x² - 8x) dx

integrate each term using the power rule

∫(a
`x^(n)`) =
`(a)/(n+1)`
`x^(n+1)` : 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