Playing with Graphs --- 2

Calculus Level 5

f ( x ) = ( x − α ) ( x − β ) ( x − γ ) ( x − δ ) \large{ f (x) = \frac{(x - \alpha)(x - \beta)}{(x - \gamma)(x - \delta)}}

You are given the function f ( x ) f(x) as described above where α , β , γ \alpha , \beta , \gamma and δ \delta are distinct real numbers.

Find the probability that the function formed is always increasing or always decreasing at any point on its graph.

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The answer is 0.333.

Aniket Sanghi by Aniket Sanghi , 21, India

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1 solution

Aniket Sanghi
Apr 26, 2016

Choose any 4 distinct values for variables.......you would be able to form 6 different equations out of which one is monotonically increasing and one is monotonically decreasing(by graph). ...Hence probability is 1/3 = 0.333

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