CPM Homework Help : CALC Problem 3-169

Use the definition of a derivative as a limit to find $f^\prime(x)$ if $f(x) = 2x + 9$ . Use the Power Rule to confirm your solution.

Hint:

Hana's definition of the derivative:

Step 1:

Substitute $f(x)$ into Hana's definition of the derivative.

Step 2:

Expand the numerator and combine like terms.

Step 3:

Factor out an $h$ from the numerator so you can 'cancel out' the $h$ from the denominator.

Step 4:

Evaluate the limit as $h →0$ . This will give you $f^\prime(x)$ .

Step 5:

Confirm that the $f^\prime(x)$ you found Algebraically agrees with what you get using the Power Rule.