Question

f(x)=2x^2; x=5, x=5+h

[2(5+h]^2]-[2(5)^2]/h
50+25h+2h^2-50/h
25h+2h^2/h
h(25+2)h
=25+2h

Where did I mess up?

Answer 1

second line should be: 50 + 20h + 2h^2 - 50 (not 25h)

Answer 2

Thanks that was a stupid mistake!

Answer 3

In these types of problems when you have to subtract two squares, make use of the identity a^2 - b^2 = (a+b)(a-b).

Answer 4

{ 2(5+h)^2 - 2(5^2) } / h = 2{ (5+h)^2 - 5^2 } / h =
2{ (5 + h + 5) * (5 + h - 5) } / h = 2 * (h+10) * h / h = h + 10

Answer 5

I will try that. I have one more of those problems hopefully I get it right

Answer 6

I forgot 2 in the last part. In the end it should be 2(h+10)

Answer 7

Can you help me with this one?

f(x) = 2 − x^2; x = 5, x = 5 + h

Answer 8

[ f(5+h) - f(5) ] / h = [ { 2 - (5+h)^2 } - { 2 - 5^2 } ] / h =
[ 2 - (5+h)^2 - 2 + 5^2 ] / h = [ 5^2 - (5+h)^2 ] / h =
[ (5 + 5 + h) * (5 - 5 - h) ] / h = (10+h)(-h) / h = -10 - h

Answer 9

Thanks for working the problems out for me, I'll keep practicing them! Thanks again for your help