Exam (elaborations)
Penn State Math 110 final questions and answers
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Penn State Math 110 final questions and answers
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Penn State Math 110 finalquestions and answers.
Demand p(x)
Revenue x(p(x))
Total Cost fixed cost-variable cost
Average Cost (C(x))/x
Profit R(x)-C(x)
Break even level R(x)=C(x)
Equilibrium point s(x)=d(x)
limits as x approaches infinity and or negative infinity or horizontal
asymptote: the powers are the same in the denominator and
numeratordivide coefficients
limits as x approaches infinity and or negative infinity or horizontal
asymptotes: the power in the denominator is bigger 0
limits as x approaches infinity and or negative infinity: the power in
the numerator is higher DNE
the chain rule f'(g(x))*g'(f(x))
, Product rule [f(x)*g'(x)]+[g(x)*f'(x)]
Quotient rule (LowDhigh-highDlow)/low^2
point slope form y-y1=m(x-x1)
derivative of e^x= e^x
derivative of e^f(x)= e^f(x) * f'(x)
ln(e)= 1
ln(1)= 0
derivative of ln(x)- 1/x
derivative of ln(f(x))= (1/f(x))*f'(x)
Critical numbers first derivative rule
Finding where the graph is increasing and decreasing: first
derivative rule
relative maximums and minimums: first derivative rule
finding where the graph is concave up or down:second derivative
rule
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