Question

Which is larger based on the graph attached inside?
a) f (3) or f (4)?

b) f(e)−f(2) or f(2)−f(1)?

c) f(2)−f(1)/2-1 or f(3)−f(1)/3-1?

d) f′(1) or f′(4)?

**for a, i think f(4) is because the slope is steeper when using the tangent. is that right? not sure about the rest though.. please explain! :)

Answer 1

the graph!!

Answer 2

f(4). f(x) is the value of y when x= a certain value. When x=3 we see that x= a lesser y value than when x=4 because the line is higher when x=4 than when x=3

Answer 3

ahh okie yay :)

what about the other ones? i'm not sure about those at all :(

Answer 4

What does e represent?

Answer 5

ln?

Answer 6

or a variable? Im not really sure :(

Answer 7

Sorry, idk.

Answer 8

ohh... i think it might just be a variable though?

Answer 9

ohhh okay yeah i think it's substituting x :/

Answer 10

a) f (4)? you know why

b) f(2)−f(1)? slope is decreasing

c) f(3)−f(1)/3-1? the slope is decreasing ... adding more interval means your avg is going to be less

d) f′(1) obvious from above two reasoning

Answer 11

for a, yes because when you put the tangent, f(4) is steeper right?

and ohhh okay :) i see :) that makes sense now...

i'll have to remember that about the intervals!!! thanks so much!!

Answer 12

no ..
use your head ... isn't the function increasing function?

Answer 13

ermm okay. hmm umm not sure then... :/ it's because they're going further than the other one?

Answer 14

on the right side ... it's not steeper ... it's steeper on the left.
but what matters is ... is your slope above horizontal or horizontal or below horizontal.

as long as your slope is above horizontal, the function is going to increase.

Answer 15

how do you define steepness?

Answer 16

ohhhh okay :)

i mean like the slope haha.. like a higher slope?

Answer 17

yes ...
which is steepest?