### Home > CALC > Chapter Ch3 > Lesson 3.2.3 > Problem 3-77

3-77.

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 *x*^{3} + *x* = 30 when *x* = 3.

*f*(*x*) = *x*^{3} + 3

*a* = 3

Notice that *f*(3) = 3³ + 3 = 30, which confirms that equation of *f*(*x*) is correct.

*f*(*x*) = *x*³ + *x* *f* '(*x*) =_______________________*f* '(3) =__________

You just avoided a lot of Algebra!