Answer:
101
Step-by-step explanation:
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
<h3>How to differentiate functions?</h3>
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
Read more about Differentiation at; brainly.com/question/5313449
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