CALCULUS Jeopardy

Value Theorems & Variation

100

If f is continuous on [a,b] and k is between f(a) and f(b), then there exists a c in [a,b] such that f(c)=k.

IVT - Intermediate Value Theorem

200

If f is continuous on [a,b], then f has a maximum and a minimum value in the interval [a,b].

EVT - extreme value theorem

300

If f is continuous on [a,b] and differentiable on (a,b), then for some c in (a,b), f'(c)=[f(b)-f(a)]/[b-a].

MVT - mean value theorem

400

y=kx has this type of variation

direct variation

500

y=k/x has this type of variation

inverse variation

Graphs

100

f(x) will have a min/max where f'(x) is _________

0 or undefined

200

f(x) is increasing when f'(x) is ________

positive

300

f(x) will be _______________, when f''(x)>0.

concave up

400

f(x) will have inflection points where ________ = 0 or undefined.

f''(x)

500

If f(x) is strictly increasing, then the left riemann sum will be an OVER/UNDER estimate for the area.

under

Derivatives

100

d/dx (5x²)

10x

200

d/dx sin(2x)

2cos(x)

300

d/dx ln(x)

1/x

400

d/dx (3x+2)⁵

5(3x+2)^4.3 = 15(3x+2)⁴

500

d/dx (tan^-1(x))

1/(1+x²)

Integrals

100

Int (cos(x)) dx

sin(x)+c

200

Int (sec²(x)) dx

tan(x)+c

300

Int (12x³) dx

3x⁴+c

400

Int (1/x) dx from 1 to 5

ln(5)

500

Int (x²+2) dx from 0 to 3

15

:)

100

How does a penguin build its house?

Igloos it together.

200

What's a frogs favorite part of calculus?

de-ribbit-ives

300

What's the integral of (1/cabin)d(cabin)?

a natural log cabin

400

2 things in calculus we never want to lose or forget...

our lims and +Cs

500

If dy/dx=ky, then y=________

ce^kt