## Exam-Style Question on Differentiation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 36. This question is similar to one that appeared on an IB Standard paper in 2013. The use of a calculator is allowed.

The function \(f\) is defined as follows:

$$f(x)=\frac{122}{1+60e^{-0.3x}}$$(a) Calculate \(f(0)\).

(b) Find a value of \(x\) for which \(f(x)=85\)

(c) Find the range of \(f\).

(d) Show that:

$$f'(x)=\frac{2196e^{-0.3x}}{(1+60e^{-0.3x})^2}$$(e) Find the maximum rate of change of \(f\).

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