Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.1 : Review : Functions
6. The difference quotient of a function f(x) is defined to be,
f(x+h)−f(x)hcompute the difference quotient for g(x)=6−x2.
Show All Steps Hide All Steps
Hint : Don’t get excited about the fact that the function is now named g(x), the difference quotient still works in the same manner it just has g’s instead of f’s now. So, compute g(x+h), then compute the numerator and finally compute the difference quotient.
g(x+h)=6−(x+h)2=6−x2−2xh−h2
Show Step 2
g(x+h)−g(x)=6−x2−2xh−h2−(6−x2)=−2xh−h2
Show Step 3
g(x+h)−g(x)h=−2xh−h2h=−2x−h