Can someone please help me???
1 answer:
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Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Equality Properties
- Reciprocals
<u>Algebra II</u>
- Log/Ln Property:
<u>Calculus</u>
Derivatives
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule:
Derivative of Ln:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Differentiate</u>
- Rewrite:
- Rewrite [Ln Properties]:
- Differentiate [Ln/Chain Rule/Basic Power Rule]:
- Simplify:
- Rewrite:
- Combine:
- Reciprocate:
- Distribute:
Answer:
1/4
Step-by-step explanation:
The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.
The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...
(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4
