Derivatives
Applications of Derivatives
Integrals
Limits
TBT
100
If f(x)=5x^3+x^2+8x, then f'(x)=
f'(x)=15x^2+2x+8
100
If x(t)=x^3+2x^2+3, when does the acceleration equal 10?
when t=1
100
∫3x+1dx
3/2x^2+x+C
100
lim┬(x→4)⁡(x^2+3+10x)
59
100
What are critical numbers?
f'(x)=0 or undefined
200
If f(x)=(x^2+8)(5x), then f'(x)=?
f'(x)=15x^2+40
200
If f'(x)=x^2-x, when is f(x) increasing
f(x) is increasing on (1,infinity)
200
∫(2x/x^2)dx
ln(x^2)+C
200
lim┬(x→2)⁡(x^2+4x-12)/(x-2)
8
200
Which derivative determines continuity?
f''(x)
300
If f(x)=(sin(2x))^2, then f'(x)=
f'(x)=4sin(2x)cos(2x)
300
If f(x)=x^3+6x^2+1, when is f(x) concave up?
f(x) is concave up on (-2, infinity)
300
∫(cosx/sinx)dx
ln(sinx)+C
300
lim┬(x→5)(x^2-3x-10)/(x-5)⁡
DNE
300
Define Continuity
lim┬(x→c+)f(x)=lim┬(x→c-)f(x)=f(c)⁡⁡
400
If f(x)=(ln(5x))(cosx), then f'(x)=?
f'(x)=-ln(5x)sinx+(cosx/x)
400
Calculate the max for f(x)=x^4-8x^2+3
f(x) has a max at x=0
400
∫(x/4+x^4)dx
1/4arctan(x^2/2)+C
400
lim┬(x→3) {x^2+2, x<3 {⁡2x^3-16x-6, x>3
11
400
The MVT states that if f(x) is cont on [a,b] and f(x) is diff on (a,b), then...
there exists a value c such that f'(c)=(f(b)-f(a))/(b-a)
500
If f(x)=(cosxsinx)/(arctanx), then f'(x)=?
(arctanx(〖cos〗^2 x-〖sin〗^2 x)-cosxsinx/(x^2+1))/(arc〖tan〗^2 x)
500
If f(x)=e^-x^2, where is f(x) concave down?
f(x) is concave down on (negative infinity, root 1/2)
500
∫(e^2cosx+1)(2sinx)dx
e^(2cosx+1)+C
500
lim┬(x→infinity)⁡(6e^4x-e^-2x)/(8e^4x-e^2x+3e^-x)
3/4
500
The IMT states that if f(x) is cont on [a,b], a does not equal b, and k is between f(a) and f(b), then there exists a value c such that
if f(x) is cont on [a,b], a does not equal b, and k is between f(a) and f(b), then there exists a value c such that f(c)=k
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