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Math 110 Exam #2 Solution Guaranteed Success Graded A+.
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To find horizontal asymptotes - correct answer take the limit as x approaches -∞ and ∞ (to do this look at dominant powers on top and bottom and remember rules) Horizontal asymptote rule : If the powers are the same - correct answer ...

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  • January 4, 2025
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  • 2024/2025
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Math 110 Exam #2
To find horizontal asymptotes - correct answer take the limit as x approaches -∞
and ∞ (to do this look at dominant powers on top and bottom and remember rules)



Horizontal asymptote rule : If the powers are the same - correct answer divide the
coefficients



Horizontal asymptote rule : If the power on the bottom is bigger - correct answer
the H.A. is y=0



Horizontal asymptote rule : If the power on top is bigger - correct answer the H.A. =
DNE (there is no H.A.)



To find Vertical Asymptotes - correct answer 1.) Simplify the function to cross out
common factors

2.) After you simplify, set the denominator = 0 and solve



From the First Derivative, f'(x) - correct answer • Critical Numbers

• Increasing / Decreasing

• Relative Extrema ( Relative Max / Relative Min )



Critical Numbers must satisfy what 2 criteria? - correct answer • f'(x) = 0 or f'(x) is
undefined

↳In other words, set top and bottom of derivative equal to 0

• Critical Numbers must be in the domain of f(x)



To find Increasing / Decreasing - correct answer Make a first derivative number line

, On first derivative number line : Wherever f'(x) is positive - correct answer f(x) is
increasing ↗



On first derivative number line : Wherever f'(x) is negative - correct answer f(x) is
decreasing ↘



To find Relative Extrema - correct answer Make a first derivative number line



On first derivative number line : Relative Maximum - correct answer Where f(x)
changes from increasing to decreasing ↗↘



On first derivative number line : Relative Minimum - correct answer Where f(x)
changes from decreasing to increasing ↘↗



(first derivative) Relative extrema can only occur - correct answer at critical
numbers



From the Second Derivative, f''(x) - correct answer • Inflection Points

• Concave Up & Concave Down

• The Point of Diminishing Returns



Inflection Points must satisfy what 3 criteria? - correct answer • f''(x) = 0 or f''(x) is
undefined

• The concavity must change at that point

• Inflection Points must be in the domain of f(x)



To find Concave Up & Concave Down - correct answer Make a second derivative
number line



On second derivative number line : Wherever f''(x) is positive - correct answer f(x) is
Concave Up

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