Find the relative minimum of y = 3x^3 + 12x^2 - 10x - 56

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Round your answers to the nearest tenth

(0.4, -57.9)

Step-by-step explanation:

y = 3x³ + 12x² - 10x - 56

dy/dx = 9x² + 24x - 10 = 0

x = [-24 +/- sqrt(24² - 4(9)(-10))]/(2×9)

x = -3.033006505, 0.3663398379

d²y/dx² = 18x + 24

For minima, d²y/dx² > 0 which is at x = 0.3663398379

y = 3(0.3663398379)³ + 12(0.3663398379)² - 10(0.3663398379) - 56

y = -57.90544608

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Explanation:

See attached for detailed workings.