a) Looks perfect!

b) Instead of writing just f(x) in the numerator, plug in the actual function expression for it (-x³ etc.). Then you can simplify a tiny bit.

c) You started correctly, with "lim[x->4]", after that comes r(x). This translates to

lim[x->4] r(x) = f'(4)

limit of r(x)

as x approaches 4

is equal to the instantaneous rate of change

at x=4

Since x **isn't equal** to 4 but only **approaches** it, the denominator (x-4) **isn't equal** to zero but only **approaches** it. How does that help? Try **factorizing** the numerator. One of its factors should be (x-4), identical to the denominator. Since (x-4) is not zero, you can divide numerator and denominator by (x-4). After that, you are able to resolve the limit by plugging in x=4

d) You might want to review these topics! Here is a list of examples:

|f(x)|f'(x)|Rule|

|:-|:-|:-|

|x^(4)|4x^(4-1)|power rule|

|x|1x^(1-1)|power rule|

|7|0|power rule (or constant rule)|

|6·x^(4)|6·4x^(4-1)|power rule, factor rule|

|-7·x|-7·1x^(1-1)|power rule, factor rule|

|6·x^(4) - 7·x|6·4x^(4-1) - 7·1x^(1-1)|power rule, factor rule, sum rule|