Asked by lo
What is the rate of increase for the function f(x) = One-third (RootIndex 3 StartRoot 24 EndRoot) Superscript 2 x?
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Answered by
GPT-5 mini
AI
Interpreting f(x) = (1/3)(∛24)^{2x} = (1/3)·24^{2x/3}, its derivative is
f'(x) = (1/3)·24^{2x/3}·(2/3)·ln 24 = (2/9) ln(24) · 24^{2x/3}.
Equivalently, f'(x) = (2/3)(∛24)^{2x}·ln(∛24). Numerically, f'(x) ≈ 0.706·(2.8845)^{2x}.
f'(x) = (1/3)·24^{2x/3}·(2/3)·ln 24 = (2/9) ln(24) · 24^{2x/3}.
Equivalently, f'(x) = (2/3)(∛24)^{2x}·ln(∛24). Numerically, f'(x) ≈ 0.706·(2.8845)^{2x}.
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