Question

Determine (a+h) - @) for f(x) = x2 + 5x and simplify.

Answer 1

Answer:

$f(a+h)-f(a)=2ah+h^2+5h$

Step-by-step explanation:

Given function is $f\left(x\right)=x^2+5x$.

Using that function, we need to determine the value of f(a+h)-f(a).

$f\left(x\right)=x^2+5x$

$f\left(a+h\right)=(a+h)^2+5(a+h)$

$f\left(a+h\right)=a^2+2ah+h^2+5a+5h$

similarly

$f\left(a\right)=a^2+5a/tex]Then [tex]f(a+h)-f(a)=(a^2+2ah+h^2+5a+5h)-(a^2+5a)$

$f(a+h)-f(a)=a^2+2ah+h^2+5a+5h-a^2-5a$

$f(a+h)-f(a)=2ah+h^2+5h$

Hence final answer is $f(a+h)-f(a)=2ah+h^2+5h$.