Given the graph of the function "f", you need to find the approximate output value:
[tex]\begin{gathered} f(3.9) \\ f(4.04) \end{gathered}[/tex]
Notice that both values are closed to:
[tex]x=4[/tex]
Therefore, you can use this formula:
[tex]f(x+\Delta x)=f(x)+f^{\prime}(x)\Delta x[/tex]
In this case, you can approximate that:
[tex]f(x)=x+c[/tex]
Where "c" is a constant.
Its derivative is:
[tex]f^{\prime}(x)=1[/tex][tex]f^{\prime}(x)=1[/tex]
(a) In order to find:
[tex]f(3.9)[/tex]
You need to use:
[tex]\Delta x=4-3.9=0.1[/tex]
Then, using the formula, you get:
[tex]f(3.9)\approx4+(1)(0.1)\approx4.1[/tex]
(b) And for the other value:
[tex]\Delta x=4-4.04=-0.04[/tex]
Then:
[tex]f(4.04)\approx4+(1)(-0.04)\approx3.96[/tex]
Hence, the answers are:
(a)
[tex]f(3.9)\approx4.1[/tex]
(b)
[tex]f(4.04)\approx3.96[/tex]
