Given ƒ(h) = 9h
3Determine the derivative ƒ'(h)
Start ƒ'(h)
Use the power rule
ƒ'(h) of ah
n = (a * n)h
(n - 1)For this term, a = 9, n = 3
and h is the variable we derive
ƒ'(h) = 9h
3ƒ'(h)( = 9 * 3)h
(3 - 1)ƒ'(h) = 27h
2
Collecting all of our derivative terms
ƒ'(h) =
27h2Start ƒ''(h)
Use the power rule
ƒ''(h) of ah
n = (a * n)h
(n - 1)For this term, a = 27, n = 2
and h is the variable we derive
ƒ''(h) = 27h
2ƒ''(h)( = 27 * 2)h
(2 - 1)ƒ''(h) = 54h
Collecting all of our derivative terms
ƒ''(h) =
54hStart ƒ(3)(h)
Use the power rule
ƒ
(3)(h) of ah
n = (a * n)h
(n - 1)For this term, a = 54, n = 1
and h is the variable we derive
ƒ
(3)(h) = 54h
ƒ
(3)(h)( = 54 * 1)h
(1 - 1)ƒ
(3)(h) = 54
Collecting all of our derivative terms
ƒ
(3)(h) =
54Start ƒ(4)(h)
Collecting all of our derivative terms
ƒ
(4)(h) =
Evaluate ƒ(4)(0)
ƒ
(4)(0) =
ƒ
(4)(0) =
ƒ
(4)(0) =
Answer
Success!
ƒ(4)(0) = 0
↓Steps Explained:↓

Final Answer
ƒ
(4)(0) =
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