CALCULUS exam 3 -SECTIONS 18-25

f’(x) of sinx

cosx

f’(x) of cosx

-sinx

f’(x) of tanx

sec²x

f’(x) of cotx

-csc²x

f’(x) of secx

secxtanx

f’(x) of cscx

-cscxcotx

CHAIN RULE

f’(x) of sin^-1x

f’(x) of cos^-1x

f’(x) of tan^-1x

f’(x) of cot^-1x

f’(x) of sec^-1x

f’(x) of csc^-1x

ln x f’(x)

1/x

b^x f’(x)

b^xlnb

log_bx f’(x)

1/(xlnb)

Linearization Approximation

It’s just the tangent line

**make sure you know how to graph this

Linear approximation/Tangent Line Approximation Function

How can this be used to estimate?

Values that would belong in the original function can be thrown into the linearization approximation to obtain approximately the value the function would show as output

How do I do notation for linearization

[value you are approximating] = original function letter (#) = new function letter (#) = new fxn with value input = answer

E.G. is in photo

when deciding your own A

choose something a little less or more than your fxn, just make it even

max/min refer to the…

y values, not the x

Local extrema are known as

relative extrema

Absolute extrema are also known as

global extrema

How to find absolute max/minimum over a function