Y= x^3 + 8x^2 +5x
work out the coordinates of the two turning points

(-5, 50) and (-1/3, -0.815)

Step-by-step explanation:

The equation is;

y = x³ + 8x² + 5x

Now the turning point will occur at where dy/dx = 0.

Thus;

dy/dx = 3x² + 16x + 5

At dy/dx = 0, we have;

3x² + 16x + 5 = 0

From quadratic formula, we can get;

x = -5 or -⅓

Thus, let's find y at this points.

y = -5³ + 8(-5)² + 5(-5)

y = -125 + 200 - 25

y = 50

Also,at x = -⅓, we have;.

y = (-⅓)³ + 8(-⅓)² + 5(-⅓)

y = -1/27 + 8/9 - 5/3

y = -0.815

Thus,the coordinates of the turning points are;

(-5, 50) and (-1/3, -0.815)

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