ShmoopTube

00:00

Thank you we sneak and here's your shmoop du jour

00:05

brought to you by capital f because lower case that

00:08

couldn't be bothered to give us time And thanks a

00:11

lot it's hard to find a new function after attacks

00:14

to be the area under the curve of Acts shown

00:18

on the interval 0 acts for an act that is

00:21

any real number What must necessarily be true about this

00:25

function f of x here the potential answers through so

00:31

this question is asking us about the function capital of

00:34

acts given lower case k f events All right so

00:37

how are these two f thing is related Well we're

00:41

told upfront capital f of x area under the curve

00:44

lower days f of x which looks exactly like the

00:47

definition of an integral which means that capital f of

00:50

x is the integral of lower case fx So now

00:54

let's start looking at our answer choices starting with anson

00:57

choice a is capital f of x discontinuous this one

01:02

seems a little tricky so we're going to take the

01:05

easy way out and look at the next answer First

01:07

we can always come back We'll just leave a trail

01:09

Of breadcrumbs Just kidding Start looking at answer choice b

01:13

from the fundamental theorem of calculus way know that wherever

01:16

fx is continuous the derivative of its integral f of

01:20

x is fx Give a little f attacks is this

01:24

continuous The derivative isn't even defined since the lower case

01:29

fx discontinuous it negative bod and for be truth But

01:34

from this logic then we know that choice d is

01:37

exactly what we've already concluded that the derivative isn't toe

01:41

find a negative five and four for the answer is

01:43

d thank goodness no need to go back to joyce

01:46

et justus Well those birds already got her pregnant well

Full Transcript