Sensitivity Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy

For

f(x)=10x

, compute the sensitivity at

x=3

with

\Delta x=0.5

and compare to

\Delta x=0.1

Solution

1
$\Delta x=0.5$ : $f(3.5)-f(3) = 35-30=5$ . Sensitivity $=5/0.5=10$ .
2
$\Delta x=0.1$ : $f(3.1)-f(3) = 31-30=1$ . Sensitivity $=1/0.1=10$ . For a linear function, sensitivity is constant ( $=$ slope) regardless of $\Delta x$ .

Answer

Sensitivity

=10

for both perturbations (constant for linear

f

)

Linear functions have constant sensitivity equal to their slope. The ratio

\Delta F/\Delta x

equals the slope

m

for any choice of

\Delta x

, since

\Delta F = m \Delta x

exactly.

About Sensitivity

In the context of functions, sensitivity measures how much the output changes in response to a small change in the input — high sensitivity means small input changes cause large output changes.

Learn more about Sensitivity →

More Sensitivity Examples

Example 1 easy

Compute the sensitivity [formula] for [formula] at [formula] with perturbation [formula].

Example 2 hard

A function [formula] is highly sensitive near large [formula]. Compare the sensitivity at [formula]

Example 4 medium

A weather model uses [formula] where [formula] is pressure. If [formula] and measurement error is [f

← All Sensitivity Examples Sensitivity Concept

Related Concepts

Rate of Change Derivative