Question

Can some help with question 2 and 4? I will post document.

Answer 1

A] Propose a value for the following
definite integral and give an interpretation
for the result : is nothing but the area under the curve from the values x=6 to x=8

Answer 2

@Akshay_Budhkar , we can find that by simply using area of a square? right?

Answer 3

yes 8^2=64 =D

Answer 4

Perfect. ;D

Answer 5

exactly..

Answer 6

aha the y-axis is degrees / hour! not degrees!

Answer 7

Lol.

Answer 8

It's not easy. haha

Answer 9

u already did :P i am trying

Answer 10

haha.

Answer 11

Amistre64 was helping me on this question but I was still lost so I was hoping if someone else also explained it maybe I would understand.

Answer 12

ok i get it

Answer 13

lets start with A

Answer 14

are you clear with A ?

Answer 15

@Akshay_Budhkar idk but i feel like we have to find some derivatives?

Answer 16

Yes I understand what you said with A.

Answer 17

@saifoo.khan yes

Answer 18

ok now let degrees be d and time be t
so on y axis we have d/t and x axis we have t
Now till x= 1 it is a straight line, with a slope -8 and intercept -8
so the equation is y=mx+c
that is y=-8x-8
that is d/t=-8t-8
d=-8t^2=8t

Answer 19

*d=-8t^2-8

Answer 20

Now for minima or maxima the first derivative of the function is o
therefore\[{d(d) \over dt }=0=-16t-8 \therefore t= 1/2\]

Answer 21

Now to find if it is a minima or a maxima we take the second derivative. if it is negative it is a maxima if positive minima ( mostly i maybe mixing them ) so in this case it is -16 which is negative. therefore it is a maxima at 1/2

Answer 22

Thank you so much I understood that! Would you be able to help me with question 4 by chance?

Answer 23

ok lemme see, is it one unit for each square right?

Answer 24

That is what I understand.

Answer 25

ok lets start with the simplest
C. f(3) = 5 any doubt?

Answer 26

Yes, thats what I see.

Answer 27

ok now A. f'(-2)
Now i believe that at a given point \[f'(x)={dy \over dx} = { y \over x}\] if we estimate. so f'(-2) =-2/-2 = 1

Answer 28

Okay, that makes sense to me.

Answer 29

for D its the same logic, area under the curve. i believe you can assume the graph to be a triangle and calculate the area

Answer 30

is it unclear?

Answer 31

So you think D would be =-2 to 4?

Answer 32

the area under the graph , from -2 to 4

Answer 33

Okay

Answer 34

Can you solve it?
For the other questions i would personally plot a graph for f'(x)

Answer 35

f"(x)=d/dx*f'(x)

Answer 36

yes i know. Now to plot the graph u must know that it is zero at minima and maxima, and u can fidn approximate values by using the approximation of y/x, and plot the graph of f'

Answer 37

then after i get the graph, f"' will be obtained by using y/x again and the last one by area under curve in that graph

Answer 38

Sorry I am just thinking. Okay, Thanks.

Answer 39

yup give it a thought, and lemme know if ustuck =D and u can tag me in some other question if u get some similar doubt =D

Answer 40

Okay, thank you so much for your help!