unit 5.1-5.7

Question 1

Mean Value Theorem

Answer 1

if f(x) is continuous on [a,b], and diferentiable on (a,b), and there is a point c where the instantaneous rate of change is equal to the avg. ROC or the slope of the tangent line between a and b

Question 2

Extreme Value Theorem

Answer 2

f(x) is continuous on the closed interval [a,b] then it has a min and a max

Question 3

Extrema (max)

Answer 3

the value of c on f(x) with an interval I, f(c) is greater than or equal to all f(x) for all values of x on the interval

Question 4

extrema (min)

Answer 4

the value of c on f(x) with an interval of I, f(c) is less than or equal to all f(x) for all values of x on the interval

Question 5

critical number

Answer 5

is f is defined at c, and f’(c) = o or is undefined/not diferentiable, then c is a critical # of f

Question 6

transition pt

Answer 6

if f’(x) transitions from increasing to decreasing or vice versa

Question 7

inflection pt

Answer 7

if f’‘(x)= 0 or undefined, ONLY if concavity changes

Question 8

concave up

Answer 8

f’(x) is increasing, f’‘(x) is positive

Question 9

concave down

Answer 9

f’(x) is decreasing, f’‘(x) is negative

Question 10

2nd derivative test local min

Answer 10

if f’‘(x) is positive at a critical number

Question 11

2nd derivative test local max

Answer 11

if f’‘(x) is negative at a critical number

Question 12

rolles theorem

Answer 12

f(x) is continuous on closed interval [a,b] and diferentiable on same Open interval, and the value f(a) = f(b) then there must be 1 value c between a,b where f’(c)=0

Question 13

intermediate value theorem

Answer 13

if f(x) exists on every value on the interval [a,b], then for any value L between f(a) and f(b) there will be a c where f(c)= that L