Verified answer

what is the value for h???? or are you meant to find the answer in terms of h?

If f(x) = 5x^2 + 2x - 5, then

[f(x+h) - f(x)] / h

= [5(x + h)^2 + 2 (x + h) - 5 - ( 5x^2 + 2x - 5)] / h

= [5x^2 + 10xh + 5h^2 + 2x + 2h - 5 - 5x^2 - 2x + 5] / h

= [ 10xh + 5h^2 + 2h ] / h

= 10x + 5h + 2

Just plug in (x+h) to get f(x+h), subtract f(x), and put it all over h:

(f(x + h) - f(x)) / h =

([5(x + h)^2 + 2(x+h) - 5] - [5x^2 + 2x - 5]) / h

Now go ahead and simplify this. You should end up with

10x + 5h + 2

Hello,

f(x+h) = f(x) with x replaced by (x+h), so we have

5(x+h)^2 + 2(x+h) -5 = 5(x^2+2xh+h^2)+2x+2h-5=

5x^2+10xh+5h^2+2x+2h-5

Now f(x+h) - f(x) = 5x^2+10xh+5h^2 +2x+2h-5-(5x^2+2x-5)=

5x^2+10xh+5h^2+2x+2h-5-5x^2-2x+5= 10xh+5h^2+2h

Now divide by h and we have 10x+5h+2.

Now to find the derivative we let h approach zero and we have.

10x+2

Hope this helps.

[f(x+h)-f(x)]/h =

{ [5(x+h)² + 2(x+h) -5 ] - (5x² + 2x - 5) }/h=

[(5x²+10xh + 5h² +2x+2h+5)- (5x²+2x-5)]/h=

(10xh+5h²+2h+10)/h=

10x+5h+2+ 10/h