drug in the blood will vary with time according to the following function: M(t ) = (e^−kt− e^−3kt), t ≥ 0 , where k> 0(a) Show that M(t ) → 0 as t →∞.(b) Show that the function M(t ) has a single local maximum, and find the maximum concentration of drug in the patient’s blood.(c) Show that the M(t ) has a single inflection point (which you should find). Does the function go from concave up to concave down at this inflection point or vice versa? Captionless Image
drug in the blood will vary with time according to the following function: M(t ) = (e^−kt− e^−3kt), t ≥ 0 , where k> 0(a) Show that M(t ) → 0 as t →∞.(b) Show that the function M(t ) has a single local maximum, and find the maximum concentration of drug in the patient’s blood.(c) Show that the M(t ) has a single inflection point (which you should find). Does the function go from concave up to concave down at this inflection point or vice versa? Captionless Image
drug in the blood will vary with time according to the following function: M(t ) = (e^−kt− e^−3kt), t ≥ 0 , where k> 0(a) Show that M(t ) → 0 as t →∞.(b) Show that the function M(t ) has a single local maximum, and find the maximum concentration of drug in the patient’s blood.(c) Show that the M(t ) has a single inflection point (which you should find). Does the function go from concave up to concave down at this inflection point or vice versa? Captionless Image
Drug Absorption A two-compartment model of how drugs are absorbed into the body predicts that the amount of drug in the blood will vary with time according to the following function: M(t ) = (e^−kt− e^−3kt), t ≥ 0 , where k> 0(a) Show that M(t ) → 0 as t →∞.(b) Show that the function M(t ) has a single local maximum, and find the maximum concentration of drug in the patient’s blood.(c) Show that the M(t ) has a single inflection point (which you should find). Does the function go from concave up to concave down at this inflection point or vice versa? Captionless Image
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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