Practice Sensitivity (Meta) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The degree to which a result or output changes in response to small changes in its inputs, parameters, or assumptions.

Is this result stable, or does a tiny change blow everything up?

Example 1

easy
Compute f(x) = x^3 at x = 2 and x = 2.1. Find the sensitivity: by what percentage does f change when x changes by 5%?

Example 2

medium
In the compound interest formula A = P(1+r)^t, compute the sensitivity of A to a small change \Delta r in the interest rate, using the derivative \frac{dA}{dr}.

Example 3

easy
For f(x)=\sqrt{x}, compute f(100) and f(104). By what percentage does f change when x increases by 4%?

Example 4

medium
A model predicts exam score S = 10\log_{10}(h) where h is hours of study. If h changes from 10 to 11 hours, compute the change in S and discuss sensitivity.
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