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What is the x-coordinate of the relative maximum of f(x) = x3 + 4x2 - 3x + 1?

User Rich Pollock
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1 Answer

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20 votes

Answer:

x = -3

Explanation:

You want the x-coordinate of the relative maximum of f(x) = x³ +4x² -3x +1.

Extrema

The x-coordinates of the relative extrema of the function will be those values of x where the derivative of the function is zero.

f'(x) = 3x² +8x -3 = (x +3)(3x -1)

The derivative is zero where its factors are zero, at x = -3 and x = 1/3.

Relative maximum

The leading coefficient of this cubic is positive, so the function values generally increase from left to right. That means the relative maximum will have the lowest x-coordinate: x = -3

The x-coordinate of the relative maximum is -3.

What is the x-coordinate of the relative maximum of f(x) = x3 + 4x2 - 3x + 1?-example-1
User Mxstbr
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