Math Test 4

Question 1

What is the mean value theorem?

Answer 1

If f is continuous and differentiable, then there exists one c such that f’(c)= f(b)-f(a)/b-a

Question 2

positive to negative is

Answer 2

local maximum

Question 3

negative to positive is

Answer 3

local minimum

Question 4

using the second derivative test, if f’‘(c) > 0, then f has a local ___ at x=c

Answer 4

local min

Question 5

using the second derivative test, if f’‘(c) < 0, then f has a local ___ at x=c

Answer 5

local max

Question 6

what does it mean if f’‘(c)>0

Answer 6

it is the local minimum

Question 7

what does it mean if f’‘(c)<0

Answer 7

it is the local maximum

Question 8

how do you find the local maximum/minimum using the second derivative test?

Answer 8

1. find such critical points of f’(c)
2. get f’‘(c) and determine