★ calc ; unit 5 methods

so many concepts omg

Extreme Value Theorem

if a function f is continuous over the interval [a,b], then f has at least one min and max value on [a,b]

f(x) is increasing when

f’(x) is positive

f(x) is decreasing when

f’(x) is negative

first derivative test: f(x)’s maximums

when f’(x) changes from pos→neg

first derivative test: f(x)’s minimums

when f’(x) changes from neg→pos

critical points

the zeros of f’(x)

canidates test

plugging in critical points and endpoints into f(x) to find the absolute min/max

f(x) is concave up when

f’’(x) is positive

f(x) is concave down when

f’’(x) is negative

point of inflection

when f’’(x) changes concavity/signs

point of inflection does not count when

f’’(x) bounces on the x-axis

there is no point of inflection when

f’’(x) is undefined

when f(x) is concave up

f’(x) is increasing

when f(x) is concave down

f’(x) is decreasing

second derivative test: f(x)’s maximums

when f’’(x) is positive

second derivative test: f(x)’s minimum

when f’’(x) is negative

in the second derivative test, you plug in cps at

f’’(x)

in the first derivative test, you plug in cps and endpoints at

f’(x)

if the second derivative test fails

conduct the first derivative test

an object is speeding up when

v(t) and a(t) have the same sign

an object is slowing down when

v(t) and a(t) have different signs

horizontal tangents are found by

dropping the x’s and solving for y

vertical tangents are found by

dropping the y’s and solving for x