Lazy Lulu is looking at this limit:
and does not want to solve it using algebra. Lulu recognizes this limit as a definition of the derivative at a point. She thinks she could use the Power Rule instead. Homework Help ✎
What variation of the definition of the derivative is this?
What is f(x) ? What is a?
Use the Power Rule to find f ′(x) and f ′(a).
This is Ana's Definition of the Derivative:
Observe that x3 + x = 30 when x = 3.
f(x) = x3 + 3
a = 3
Notice that f(3) = 3³ + 3 = 30, which confirms that equation of f(x) is correct.
f(x) = x³ + x
f '(x) =_______________________
f '(3) =__________
You just avoided a lot of Algebra!