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nekit [7.7K]
3 years ago
13

Find the relative minimum of y = 2x 3 + 14x 2 - 10x - 46

Mathematics
2 answers:
nikitadnepr [17]3 years ago
7 0

Answer:

The minimum value is 47.704  when x = 1/3 correct to the nearest thousandth.

Step-by-step 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.

miss Akunina [59]3 years ago
3 0
The answer is x= 23/12 OR x=1 11/12 OR x=1.916
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By looking at this equation, I can identify that the answer must be within the first quadrant since the numerator and denominator are both positive.

Since it is in the first quadrant, the range of the value of the answer must be between 0 degrees less than or equal to x less than or equal to 90 degrees.

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*Use the attachment for reference

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