Answer:
[tex]m'(4)=2.5[/tex]
Explanation:
The given function m, is defined by [tex]m(g(x))=x[/tex].
This means m and g are inverse functions.
We want to find m'(4).
We differentiate [tex]m(g(x))=x[/tex] using the chain rule to get:
[tex]m'(g(x))\cdot g'(x)=1[/tex]
When x=2, we obtain:
[tex]m'(g(2))\cdot g'(2)=1[/tex]
From the table, [tex]g(2)=4[/tex] and [tex]g'(2)=0.4[/tex]
We substitute to get:
[tex]m'(4)\cdot 0.4=1[/tex]
Divide by 0.4
[tex]m'(4)=\frac{1}{0.4}[/tex]
[tex]m'(4)=2.5[/tex]
