Answer:
The minimum value is 47.704 when x = 1/3 correct to the nearest thousandth.
Explanation:
y = 2x^3 + 14x^2 - 10x - 46
To find the turning point(s) on the curve we first differentiate:
dy/dx = 6x^2 + 28x - 10 This = zero for turning points:
6x^2 + 28x - 10 = 0
2(3x^2 + 14x - 5) = 0
(3x - 1 )(x + 5) = 0
x= 1/3, - 5.
We now determine the nature of the turning points:
The second derivative is 12x + 28
When x = 1/3 it's value is positive.
When x = -5 its value is -60 + 28 which is negative.
So x = 1/3 gives a relative minimum.
When x = 1/3, y = -47.704.