Is there a function f with f(1) = -2, f(3) = 0, and f'(x) > 1 for all x?

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Is there a function f with f(1) = -2, f(3) = 0, and f'(x) > 1 for all x?

2007-09-24 00:50:30 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

No. Since f(1) = -2 and f(3) = 0, you certainly do not have f(x) > 1 for all x.

2007-09-24 01:06:16 · answer #1 · answered by Tony 7 · 0⤊ 1⤋

No.

The slope of the line between the two given points is (0 - -2) / (3 - 1) or 1.

In order for the f'(x) > 1 for all x's, the slope of a line between any two points on the curve of the function would also have to be > 1.

2007-09-24 08:31:35 · answer #2 · answered by PeterT 5 · 1⤊ 0⤋