For normal goods, the Engel curve has a positive gradient.
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Still another region of positive gradient occurs at very high altitudes, in the aptly-named thermosphere above.
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In other words, there is a "'steeper negative gradient "'than positive gradient.
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In the case of an applied electrostatic field, an electron will deflect towards the positive gradient of the field.
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So I'm going to assume your requirement is satisfied if f ( x ) has strictly positive gradient when " x " is negative and has strictly negative gradient when " x " is positive.
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