Vitamin E Injection

Calculation exponentially?
When a drug or vitamin is administered intramuscularly, the concentration in the blood at the time after injection is not f (t) = 5 (e ^ (-0.1t) – E ^ (-0.51t)) Find the value of t where the function is at its peak once set to 0, How to solve it, how to solve it to 0 when 0 = [0.1e ^ - (- 0.1t) + 0.51e ^ (-0.51t)]
f (t) = 5 [e ^ (-0.1t) - e ^ (-0.51t)] f '(t) = 5 [(-0.1) e ^ (-0.1t) + 0.51e ^ (-0.51t)] find the min / max to f' (t) = 0 (0.51) e ^ ( -0.51t) = (0,1) e ^ (-0.1t) …. Now take the logarithm of both sides in (0.51) – 0.51t = ln (0.1) – In 0.1t (5.1) T = 0.41t = ln (5.1) / 41 t ≈ 3, 97 f''(t) = 5 [(0.01) e ^ (-0.1t) - 0.2601 e ^ (-0.51t)] f''(3.97) ≈ -0.13 <0, so that is a maximum. Answer: t ≈ 3.97
NAGOYA The vitamin cocktail, intravenous injection multi vitamin complex
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