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Calculus: Substituting in Values to Determine General Trend

#5
Let p(x) = x3 -ax, where a is constant
a) If a<0, show that p(x) is always increasing.
substituting in values

b) If a>0, show that p(x) has a local maximum and a local minimum.

c) Sketch and label typical graphs for the cases when a<0 and when a>0.

Find the value(s) of x for which:
a) f(x) has a local maximum or local minimum. Indicate which ones are maxima and which are minima.
b) f(x) has a global maximum or global minimum
#6
f(x) = x10 - 10x, and 0 <= x <=2

#8
As an epidemic spreads through a population, the number of infected people, I, is expressed as a function of the number of susceptible people, S, by
I=k ln(S/S0) - S + S0 + I0, for k, S0, I0 > 0.

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Let p(x) = x^3 -ax, where a is constant

a) If a<0, show that p(x) is always ...

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Neat, step-by-step solutions using graphs are provided.

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