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How do you find an AVERAGE rate of change of a function f(x) on the interval [a,b]?
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f(b)-f(a)/b-a
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How do you find an instantaneous rate of change of a function f(x) at a point?
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Find f'(x) and plug in the coordinates of the point.
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How do you find the derivative using the limit process?
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f'(x)=lim f(x+a)-f(x)/a
x-a
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What are the rules for horizontal asymptotes?
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If the degree on top is larger...then none.
If the degree on top is smaller....then zero.
If the degrees are the same on the top/bottom...then ratio of lead. coefficients.
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What is removable discontinuity?
Describe analytically & graphically.
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Analytically....you can remove common factors.
Graphically....there is a hole in the graph.
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What is nonremovable discontinuity?
Describe analytically & graphically.
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Analyticall....you cannot remove common factors.
Graphically....there is no way to make the function continuous (vertical asymptote, jump, oscilation.)
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When does a limit exist?
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When the limit from the right equals the limit from the left.
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How do you find vertical asymptotes?
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Factor the rational expression and look at the factors in the denominator. If no factors cancel with the numerator then the vertical asymptotes are the values of x that make the denominator equal to zero.
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How do you find the slope of a normal line?
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Find the slope of the tangent line and take the negative reciprocal.
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What is displacement?
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The change in position over time. (Delta s)
The antiderivative of velocity.
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What is velocity?
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The derivative of position or the antiderivative of acceleration.
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What is acceleration?
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The derivative of velocity.
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How do you find total distance traveled when given a velocity function?
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Integrate the absolute value of velocity.
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How do you find the displacement of an object when given a velocity function?
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Integrate the velocity function.
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What is the process when differentiating implicitly?
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1. Differentiate both sides with respect to x. (Remember to attach a y prime when differentiating y terms.)
2. Collect y prime terms on the left side of the equation.
3. Factor out y prime.
4. Solve for y prime.
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