### Home > APCALC > Chapter 5 > Lesson 5.2.4 > Problem5-99

5-99.

For the following functions, determine f(x), c, f ′(x), and f ′(c). Homework Help ✎

1. $f ^ { \prime } ( c ) = \operatorname { lim } _ { \Delta x \rightarrow 0 } \frac { ( 5 - 3 ( 1 + \Delta x ) ) - 2 } { \Delta x }$

This is Hana's Definition of the Derivative. Notice that Δx is equivalent to h.

f(x) = 5 − 3x where c = 1
so f '(x) = −3 and f '(1) = −3

2. $f ^ { \prime } ( c ) = \operatorname { lim } _ { \Delta x \rightarrow 0 } \frac { ( - 2 + \Delta x ) ^ { 3 } + 8 } { \Delta x }$

See hint in part (a).

3. $f ^ { \prime } ( c ) = \operatorname { lim } _ { x \rightarrow 9 } \frac { 2 x ^ { 1 / 2 } - 6 } { x - 9 }$

This is Ana's Definition of the Derivative.