Calc unit 2
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Last updated 9:49 PM on 10/25/25
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13 Terms
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Average Rate of Change
Has 2 points, The slope of the secant line from x=a to x=a+h.
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Instantaneous Rate of Change
Has 1 point. The slope of the Tangent line at x=a.
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Equation of the Tangent line- Taylors form:
y = y1 + m ( x - x1 )
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Differentiability
We can find the derivative. Must be a smooth line or curve. The derivative fails to exist where the function has: Discontinuity, Vertical Tangent line, and sharp turns.
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Normal Lines
Perpendicular to the Tangent line. Opposite and reciprocal slope
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\frac{d}{dx}a^{x}=
a^{x}\cdot\ln a
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\frac{d}{dx}\exponentialE^{x}=
\exponentialE^{x}
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