Answer:
Final answer is 7.
Step-by-step explanation:
Given that f(x) =7x+8.
Now we need to find the derivative of f(x) at x=5
So let's find derivative first.
[tex]f(x)=7x+8[/tex]
[tex]f'(x)=\frac{d}{dx}(7x+8)[/tex]
[tex]f'(x)=\frac{d}{dx}(7x)+\frac{d}{dx}(8)[/tex] {Using formula [f+g]'=f'+g'] }
[tex]f'(x)=7\frac{d}{dx}(x)+\frac{d}{dx}(8)[/tex] {Using formula f'(ax)=a f'(x) }
[tex]f'(x)=7(1)+0[/tex] {derivative of constant term is 0 }
[tex]f'(x)=7[/tex]
Now plug the given value of x=5
[tex]f'(5)=7[/tex]
Hence final answer is 7.
