A curve has the equation y=x3+8x²+5x.
Work out the coordinates of the two turning points.

Answer:
f(x) = x³ + 8x² + 5x
f'(x) = 3x² + 16x + 5 = 0
(x + 5)(3x + 1) = 0
x = -1/3, x = -5
f(-5) = (-5)³ + 8(-5)² + 5(-5) = 50
f(-1/3) = (-1/3)³ + 8(-1/3)² + 5(-1/3) = -22/27
The coordinates of the two turning points are (-5, 50) and (-1/3, -22/27).