Given:
The function is
[tex]f(x+2)=2x+3[/tex]
To find:
The value f'(4).
Solution:
We have,
[tex]f(x+2)=2x+3[/tex]
Putting [tex]x+2=t[/tex] and [tex]x=t-2[/tex] we get
[tex]f(t)=2(t-2)+3[/tex]
[tex]f(t)=2t-4+3[/tex]
[tex]f(t)=2t-1[/tex]
Differentiate with respect to t.
[tex]f'(t)=2(1)-0[/tex]
[tex]f'(t)=2[/tex]
At [tex]t=4[/tex], we get
[tex]f'(4)=2[/tex]
Therefore, the value of f'(4) is 2.
