MATH 205 FINAL EXAM Latest Update 2024-2025 Questions and 100% Verified Correct Answers Guaranteed A+
(a,b) - CORRRECT ANSWER: parenthesis- end points *not included*
[a,b] - CORRRECT ANSWER: brackets- end points *included*
absolute maximum - CORRRECT ANSWER: value at the highest point of the graph
absolute minimum - CORRRECT ANSWER: value at the lowest point of the graph
acceleration - CORRRECT ANSWER: f"(x)
adding/subtracting fractions with unlike denominators - CORRRECT ANSWER: multiply all the term by the LCD
area between two curves - CORRRECT ANSWER: top function minus the bottom
function
as limit approaches infinity - CORRRECT ANSWER: when highest degree in numerator: infinity
when highest degree in denominator: 0
same degree: numerical coefficients
Average cost - CORRRECT ANSWER: divide an x out of cost function
c(x) with bar on top
average of the function - CORRRECT ANSWER: (1/b-a) multiplied by f(x)
average velocity - CORRRECT ANSWER: distance traveled / time elapsed
Chain rule - CORRRECT ANSWER: take the exponent , move it to the front, keep the inside term and raise it to the prior power minus one, multiplied by the derivative of the inside term
common log - CORRRECT ANSWER: logx
concave down - CORRRECT ANSWER: tangent line slopes getting smaller /---\
f"(x) < 0
concave up - CORRRECT ANSWER: tangent line slopes getting bigger |___|
f"(x) > 0
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continuous functions - CORRRECT ANSWER: all constant functions (y=2)
the identity function (y=x) all polynomial functions all rational functions (except where denominator = 0)
cost - CORRRECT ANSWER: c(x)
derivative - CORRRECT ANSWER: slope of the tangent line
instantaneous rate of change
differentiability and continuity - CORRRECT ANSWER: if a function is not continuous at a point, then it is *not* differentiable at that point.if a point is continuous at a point, then it may or may not be differentiable at that point.points that are abrupt direction changes are not differentiable.points that have vertical tangents are not differentiable if a function is differentiable at a point, then it is continuous
distance - CORRRECT ANSWER: f(x)
domain in a radical - CORRRECT ANSWER: greater or equal to 0
domain of a fraction - CORRRECT ANSWER: denominator cannot equal 0
domain of fraction with radical in denominator - CORRRECT ANSWER: greater than 0
exponential growth and decay - CORRRECT ANSWER: Qo is start amount
Q(t) is end amount k is the growth/decay constant
f(x) is decreasing - CORRRECT ANSWER: tangent slopes are negative
f'(x) < 0
f(x) is increasing - CORRRECT ANSWER: tangent slopes are positive
f'(x) > 0
factoring a trinomial with a numerical coefficient - CORRRECT ANSWER: 1. put it in descending order
- if there is a gcf, factor it out
- multiply leading coefficient the constant term (first and last term)
- with that product, list factors that when added, will give you the middle term
horizontal asymptotes - CORRRECT ANSWER: when denominator cannot = 0
inflection point - CORRRECT ANSWER: any point on graph where the tangent line
exists and the concavity changes
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