Q. 10 - Calculus

Question

Preview of Differential Equations: 

Given each of the following equations involving a function f, find a possible formula for f(x).

$f\text{'}\text{'}\left(t\right)=\cos t$

Step-by-Step Solution

Answer

The possible formula for the function $f\text{'}\text{'}\left(t\right)=\cos t$ is $f\left(t\right)=-\cos t$.

Step 1. Given Information.

The function: 

$f\text{'}\text{'}\left(t\right)=\cos t$

Step 2. Consider the function.

Consider the function,

$$\begin{gathered} f\left(t\right)=-\cos t \\ f\text{'}\left(t\right)=\frac{d}{dt}(-\cos t) \\ =\sin t \\ f\text{'}\text{'}\left(t\right)=\frac{d}{dt}(\sin t) \\ =\cos t \end{gathered}$$

So the function is $f\left(t\right)=-\cos t$.