Question

Hey i keep on getting these questions wrong on my math hw and i was wondering if anyone could explain to me how to do them

Answer 1

given

$\frac{f(x + h) - fx}{h}$

substitute the value given into the equation

$= \frac{5(x + h) ^{2} }{h} - 5 {x}^{2}$

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

thus simplifying the numerator only

$= \frac{5 {x }^{2} + 10xh + 5 {h}^{2} - 5 {x}^{2} } {h}$

$= \frac{10xh + 5 {h}^{2} }{h}$

$= 10x + 5h$