find (f(x + h)-f(x))/h for the given function. f(x)=x² + 5x. 2x + 5 2x + h + 5 1 2xh+h² + 5

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: $f(x + h)=(x + h)^2+5(x + h)=x^{2}+2xh+h^{2}+5x + 5h$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(x^{2}+2xh+h^{2}+5x + 5h)-(x^{2}+5x)$ $=x^{2}+2xh+h^{2}+5x + 5h - x^{2}-5x=2xh+h^{2}+5h$

Step3: Calculate $\frac{f(x + h)-f(x)}{h}$

$\frac{f(x + h)-f(x)}{h}=\frac{2xh+h^{2}+5h}{h}$ Factor out $h$ from the numerator: $\frac{h(2x + h+5)}{h}=2x + h+5$

Answer:

B. $2x + h + 5$