Question

use lim = f(h+a)-f(a)/h to find the derivative
h->0

f(x)=2x^3 a=10

Answer 1

I got 6000 but that doesn't seem right

Answer 2

can you post what you did ?

Answer 3

2(10+h)^3-8000/h= 8000+8h^3-2000/h

Answer 4

the h cancels the cube and makes it a square 8000+8h^2-2000 and since h is going to 0 than 8h^2 is 0 and when you combine 8000-2000 you get 6000

Answer 5

I got 600

Answer 6

isn't 10*10*10= 1000

Answer 7

I'll post it - I might have a mistake.

Answer 8

\[\frac{1}{h}*(2(h+a)^3-2a^3)\]
\[=\frac{1}{h}*(\cancel{2a^3}+6a^2h+6ah^2+h^3-\cancel{2a^3})\]
\[=6a^2+6ah+h^2\]

\[\lim_{x \rightarrow 0} 6a^2+6ah+h^2=6a^2=6*10^2=600\]

Answer 9

in the lim above it should be h->0 not x->0 obviously :)

Answer 10

alright thanks