Theorems and chapter three

Question 0

The mean value theorem

Answer 0

If function f is continuous on the closed interval a,b and differentiable on the open interval a,b then for some value C between a and b,
f’c=f(b)-f(a)/b-a

**once you find it this way, set the derivative equal to f’c to find x

Question 1

Rolles Theorem

Answer 1

If function f is continuous on the closed interval a,b and differentiable on the open interval a,b and f(a)=f(b) then for some value between a and b f’(c)=0

Question 2

Extreme value theorem

Answer 2

remLet f be a continuous function on the closed and bounded interval a,b. then f assumes both a max and min value somewhere on a,b

Question 3

To find whether an object is speeding up or slowing down,

Answer 3

velocity and acceleration must have different signs

Question 4

To find absolute max and min, use

Answer 4

EVT

use the end points of the interval and the critical values

Question 5

Concave up if

Answer 5

f’‘(x) is greater than 0

Question 6

Concave down if

Answer 6

f’‘(x) is less than 0