A Holling’s type III response assumes that the consumer is limited by its ability to process/handle food. It also assumes that at low food densities, consumption accelerates as food density increases. A Holling’s type III functional response can be modeled by the equation C(x)=ax^2/1+abx^2.

Show that C(x) is accelerating for low food densities and decelerating for large food densities. To do this, find a value x = a such that C''(a) = 0, C''(x) > 0 for 0 < x < a, and C''(x) < 0 for x > a.

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