AP Calculus AB Unit 1

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4 Terms

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Derivative of the inverse

dy/dx [g(x)]=1/[f’(x)] at a point dy/dx[g(a)]=1/[f’(b)]

Where g(x) is the inverse of f(x) (not using f-1(x)

<p><span>dy/dx [g(x)]=1/[f’(x)] at a point </span>dy/dx[g(a)]=1/[f’(b)]</p><p><span>Where g(x) is the inverse of f(x) (not using f<sup>-1</sup>(x)</span></p>
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Interval

Ex: [x, x2]

Means what happens during that range

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Secant line

average rate of change over an interval

Secant (average) is only good for certain things, ie. secant of of sinx is 0

<p>average rate of change over an interval</p><p>Secant (average) is only good for certain things, ie. secant of of sinx is 0</p>
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Equivalence Conditions

  • Instantaneous rate of change (ROC) at x2 is the equivalent of finding

  • The derivative at x2 which is

  • Equivalent to the slope of the tangent line at x2

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