Question

The temperature of a liquid during an experiment can be modeled by the function f(x)=3.8cos(πx/20)+2.2 , where f(x) is the temperature in °C and x is the number of minutes into the experiment.

What is the lowest temperature the liquid reached during the experiment?

Round to the nearest tenth of a degree if needed.

Use 3.14 for π .

Answer 1

The temperature of the liquid during the experiment is
`-1.6^oC`

Explanation:

Minimum Value Of Functions

The absolute minimum of a function f exists only if no other value of f is lower than the minimum in the domain of f. There can be more than one minimum value, like in the case of sinusoid functions. The sine and cosine functions have an oscillating nature, with values ranging from 1 to -1. The function given in the problem is

`f(x)=3.8cos(\pi x/20)+2.2`

The minimum value of the temperature f(x) will occur when the cosine is at its minimum, i.e. when it goes to -1. Thus

`f_(min)=3.8(-1)+2.2`

`\boxed{f_(min)=-1.6^oC}`

The lowest temperature of the liquid during the experiment is -1.6^oC