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Section 1

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the 2nd derivative test f'(a)=0 and f''(a)>0

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Calculus Math

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Section 1

(44 cards)

the 2nd derivative test f'(a)=0 and f''(a)>0

Front

What do we know about x=a on f

Back

Acceleration

Front

in terms of position/velocity

Back

Antiderivative of sinx

Front

-cosx + c

Back

d/dx (cosx)

Front

-sinx

Back

Definition of Derivative f'(x)

Front

involves h and limit h->0

Back

Antiderivative of e^x

Front

e^x + C

Back

Antiderivative of cscxcotx

Front

-cscx + C

Back

If f is differentiable at x=a

Front

Continuity/ lim h->0 of derivative exists (write out)

Back

The graph of f changes concavity

Front

what does f, f', f'' do or look like

Back

d/dx (sinx)

Front

cosx

Back

Antiderivative of cosx

Front

sinx + c

Back

d/dx (cotx)

Front

-csc^2x

Back

d/dx (cscx)

Front

-cscxcotx

Back

Definition of Derivative f'(a)

Front

no h, x->a

Back

f''(x)>0 for a<x<b

Front

what does f and f' do on interval

Back

Antiderivative of secxtanx

Front

secx + c

Back

d/dx (e^x)

Front

e^x

Back

f'(x) is decreasing for a<x<b

Front

what does f and f'' do on interval

Back

Antiderivative of csc^2x

Front

-cotx+c

Back

instantaneous rate of change of f at x=a

Front

slope of the tangent line

Back

d/dx (loga(x))

Front

base a

Back

Antiderivative of x^(n)

Front

x^n+1/n+1+C

Back

An object is at rest when...

Front

think velocity

Back

f'(x)<0 for a<x<b

Front

whats f doing on the interval

Back

Antiderivative of sec^2x

Front

tanx + C

Back

Velocity

Front

in terms of position

Back

d/dx (kf)

Front

prime notation

Back

d/dx (f +/- g)

Front

Prime notation

Back

Difference Quotient for f f=x

Front

Not a limit, involves h and no x

Back

the 2nd derivative test f'(a)=0 and f''(a)<0

Front

What do we know about x=a on f

Back

critical points of f

Front

3 things: thin endpoints, and f'

Back

d/dx (tanx)

Front

sec^2x

Back

d/dx (f)(g)

Front

product rule

Back

Velocity is constant when...

Front

think acceleration

Back

d/dx (f(g(x))

Front

Chain rule

Back

d/dx (f/g)

Front

quotient rule

Back

d/dx (a^x)

Front

a^xln(a)

Back

f'(x) is increasing for a<x<b

Front

what does f and f'' do on interval

Back

f'(x)>0 for a<x<b

Front

whats f doing on the interval

Back

Average Rate of Change of f(x) on [a,b]

Front

f(b)-f(a)/b-a

Back

d/dx (secx)

Front

secxtanx

Back

f''(x)<0 for a<x<b

Front

what does f and f' do on interval

Back

Antiderivative of a^x

Front

a^x/ln(a) + C

Back

d/dx (x^a)

Front

Power rule

Back