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10 cards from this deck
The tangent slopes are negative in that region.
Use the first derivative: f′(x)<0f'(x) < 0f′(x)<0.
f′(x)=6x−6x2=6x(1−x)f'(x) = 6x - 6x^2 = 6x(1 - x)f′(x)=6x−6x2=6x(1−x).
Solve x(6−6x)<0x(6 - 6x) < 0x(6−6x)<0.
f(x)f(x)f(x) is decreasing for 0<x<10 < x < 10<x<1.
Show that f′(x)>0f'(x) > 0f′(x)>0 for all xxx in its domain.
f′(x)=1/(1−x)2f'(x) = 1/(1-x)^2f′(x)=1/(1−x)2 using the quotient rule.
f′(x)=1/(1−x)2f'(x) = 1/(1-x)^2f′(x)=1/(1−x)2 for x<1x < 1x<1.
The function is increasing in its domain.
They help determine increasing or decreasing behavior.
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