Mathematics OpenStudy (anonymous):

f(x) = x^3 - x; using increment form of the definition of derivative, find f'(x). OpenStudy (anonymous):

as in $f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$?? OpenStudy (anonymous):

i am not familiar with the term "increment form" OpenStudy (anonymous):

yes that one pretty sure OpenStudy (anonymous): OpenStudy (anonymous):

ok lets to it OpenStudy (anonymous):

$f(x)=x^3-x$ $f(x+h)=(x+h)^3-(x+h)$ then algebra $f(x+h)=(x+h)^3-(x+h)=x^3+3x^2h+3xh^2+h^2-x-x$ OpenStudy (anonymous):

damn typo $f(x+h)=(x+h)^3-(x+h)=x^3+3x^2h+3xh^2+h^2-x-h$ OpenStudy (anonymous):

now $f(x+h)-f(x)=x^3+3x^2h+3xh^2+h^2-x-h-(x^3-x)$ $=3x^2h+3xh^2+h^3-h$ OpenStudy (anonymous):

and finally $\frac{f(x+h)-f(x)}{h}=\frac{=3x^2h+3xh^2+h^3-h}{h}=\frac{h(3x^2+3xh+h^2-1)}{h}$ $=3x^2+3xh+h^2-1$ now take the limit as h goes to zero (be replacing h by zero) and you get $3x^2-1$ just like it should be OpenStudy (anonymous):

hope all the steps are there i see the binary dust is coming, so i will go watch judge judy

Latest Questions NewThingz: help?
3 seconds ago 15 Replies 0 Medals ShadowKitten21: how do you guys rate my photoshop that i did in LO DAAD Lab
5 minutes ago 10 Replies 2 Medals winteramina2003: How do you make a testimonial on someone's account? i'm still new to how things w
12 minutes ago 3 Replies 1 Medal baker490027: Why when u try to keep it 100 and do sum good for ah change y is someone always gotta bring you down.
3 minutes ago 6 Replies 0 Medals baker490027: Check dis ask yo self is you real or fake????! do you sell ah nih dream or do you
4 minutes ago 33 Replies 5 Medals jordynwillman: Who was Adam Smith and what were his ideas?
54 minutes ago 6 Replies 1 Medal baker490027: i jus got sum mo ack from G\$ plug now im actin lazy bought ah 100 i bought ah k w
35 minutes ago 80 Replies 2 Medals baker490027: my feee ain wanna give me nun she said im actin famous told my mama i sold my fir
35 minutes ago 10 Replies 2 Medals clor2006: Anneli is painting a calm seascape on a clear spring day. What type of colors wil
48 minutes ago 35 Replies 1 Medal clor2006: 1) Do you think the Ten Commandments changed how the Hebrews lived their daily li
1 hour ago 0 Replies 0 Medals