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Approximation techniques
Linearizations and differentials
Linearization purpose
To approximate a function value
Differential purpose
To approximate change
Concave up
Tangent below the curve: under-approx
Concave down
Tangent above the curve: over-approx
Dx
Independent variable-small change in x
Dy
dy=f'(x)dx-small change in y
d/dx sin x
cos x
d/dx cos x
-sinx
d/dx tanx
sec²x
d/dx cotx
-csc²x
d/dx secx
secxtanx
d/dx cscx
-cscxcotx