# AP Calc help plz!!!!?

The curve y = x^3 + x^2 - x has two horizontal tangents. Find the difference in height of these two horizontal lines.

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- daSVgrouchLv 77 years agoFavorite Answer
y'(x) = 3x^2 + 2x - 1 = 0 at the tangents

solve for the two values of x, (x = -1 and x = 1/3)

plug them into y(x) and then subtract the differences

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- 7 years ago
A horizontal tangent is defined as a point where the derivative is zero.

y'=3x^2+2x-1

Factored: (3x+1)(x-1)=y'

y'=0 at x=-1/3 and 1

When you plug in those numbers to the original curve you get (-1/3,11/27) and (1,1)

Then you subtract their y values.

1-11/27=16/27

Therefore, 16/27 should be the difference in height.

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- Anonymous7 years ago
the difference in height of these two horizontal lines = f(-1)-f(1/3)

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