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

`(f(x + h) - fx)/(h)`

substitute the value given into the equation

`= (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`