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If f(x + 2) = 2x + 3 then find f-'(4).​

Sagot :

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.

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