Question

Help Please with Average rate

Answer 1

You know how to find the slope of a line?

Answer 2

rise/run?

Answer 3

yes...exactly

Answer 4

so -3/3?

Answer 5

or is it -3/4 @anikhalder

Answer 6

now..average rate in this question simply means that you'll have to find in the indicated figure the slope between the two points given ( rise / run ). Not just this figure( which here resembles an upside down U...parabola the mathematicians call it..) but in any question when you are asked to find the average rate..just find rise/run

Yes it will be -3/4...well done Stacy :)

Answer 7

Thank you very much @anikhalder can you help me with one more?

Answer 8

I'll try my best...:)

Answer 9

Thank you :)... I did this one however it tells me that my answer is wrong

Answer 10

well, do you know this:

Average = \[\frac{ f(x _{2} )-f(x _{1})}{ x _{2}-x _{1} }\]

where x2= final value of x
x1= initial value of x

Answer 11

I do but I came up with that answer 144+4h

Answer 12

i presume the answer would be something like 24 + h... please check whether i'm right or wrong

Answer 13

it says that answer is wrong

Answer 14

:P.. okay let's check...what do we get when we place x2 as (3+h) and solve for f(x2) ?

Answer 15

what do you mean

Answer 16

hmm..put the answer as 8h please and tell me whether it's right or wrong

Answer 17

wrong again :(

Answer 18

i am dead...:P anyway..i was thinking about something else..forget it..

So back to the topic..we need to find the average right? so first tell me what will be the value of f(3+h)

Answer 19

yes we have to find the average rate

Answer 20

and do we just plug 3+h in 4(3+h)^2

Answer 21

hey wait..hold..please put the answer as 8 and tell me if it's right or wrong

Answer 22

wrong again and it locked in so I can't continue well thanks anyway

Answer 23

can you help with quadratic functions?

Answer 24

Anyway..i'm sorry couldnt be of any help..but i am not sure whether the question is asking average or the average rate of change

Answer 25

average rate of change

Answer 26

yes..but don't keep your hopes too high...see my condition..:P pathetic me

if its average rate of change of function then i presume we got to differentiate that

Answer 27

hold on..@hartnn ...can you please help us here

Answer 28

its fine I had all the other questions fine

Answer 29

okay..but we need to solve this one...suppose it comes up in your exam..what to do then?

Answer 30

@hartnn please help

Answer 31

understood but I came up with 144+4h as my final answer

Answer 32

wait..the moderator is here..he will surely help us out..let's wait for his reply

Answer 33

Will do

Answer 34

where is he?

Answer 35

want to skip to the next one till he comes

Answer 36

sure

Answer 37

hmm...this time i think we can work this out..do you know differentiation?

Answer 38

what do you mean

Answer 39

hmm..well...it's like finding the derivative of the equation..

finding the derivative of an equation is like finding the tangent or slope of the equation...do you know that?

Answer 40

sort of haha

Answer 41

that's great!

So let's find the derivative of this equation..what shall be the derivative when we differentiate this equation with respect to x?

Answer 42

would it be 3-2x?

Answer 43

nope its wrong my bad

Answer 44

\[\frac{ d }{ dx} (6 +3x - x ^{2}) = 3 - 2x\]

Answer 45

wait..you are wrong..then i'm wrong as well..:P

Answer 46

it has to be a final exact number answer

Answer 47

yes..wait..it's not over..

Answer 48

now we have found the tangent...the given equation is a parabola...at the maximum or minimum position of the parabola the slope of the equation has to be zero

i.e. 3-2x = 0

Answer 49

i mean the slope of the 'tangent' should be zero..not the 'equation'...sorry

Answer 50

so 0 would be our final answer?

Answer 51

no no no

Answer 52

now from this equation solve for x..what do we get?

Answer 53

-3/-2 to 3/2 = 1.5?

Answer 54

yes! x=1.5

(but it's not yet over)

this means that when x=1.5 the equation reaches it's max or min value...so now put x=1.5 back into the original equation and let's find out the value...what do we get

Answer 55

8.25?

Answer 56

yes..please tell me this time that this would be the answer.._/\_

Answer 57

YESSSSS! haha

Answer 58

now i can die in peace..:) lol

Answer 59

haha I have one more if you don't mind :)

Answer 60

okay..:) i'll try my best

Answer 61

i think this time as well we have to do the same thing...we just have to write the value of x at which the max or min occurs...you might be confused that last time we had to write mx Or min..but this time we have been asked to write both max AND min...have no fear..differntiation is here...when we differentiate we'll get a quadratic equation instead of a linear equation (unlike last time)..this equation shall be the the tangent and we will have to equate it to zero...as it would be a quadratic equation we'll find 2 values of x..one would be the max, another the min...

to cut the long story short...first let's differentiate and find the slope's equation

Answer 62

so it would be -3x^2+2x+1

Answer 63

yeah!..now we put this to zero and find the values of x

Answer 64

how would I do that I'm trying but my assumption won't calculate to 0

Answer 65

do you know how to solve a quadratic equation? by factorisation?

Answer 66

would x = 1,-1/3?

Answer 67

yes!

Now...i did a mistake previously ( i think so)
Let me tell you what..i told you that these 2 values will be one for maxima and another for minima...it's not so..we have to find that out...for finding that out we will have to find the rate of change of slope of the tangent...
i.e. slope of the slope (that we found out)
i.e we will have to differentiate the quadratic eqn that we found out and put the 2 values of x each time after differentiating...tell me after you do this

Answer 68

so you just want me to input the X's we got into the equation?

Answer 69

no first differentiate the equation you solved...and then input the X's you got into the derivative

Answer 70

got -1 from both

Answer 71

how?

Answer 72

wait my bad 2-6x correct?

Answer 73

yes...now put the x's in this and tell me the values

Answer 74

-4 and 4

Answer 75

yep! now you see when we put x=1..we get -4, which is a negative value...when we get a negative value it means we have found the MAXIMA

and when we put x=-1/3 we get +4 which is a positive value...when we get a positive value it means we found the MINIMA

So, the value of the local maxima will be found when you put x=1 in the original eqn

and the local minima will be found when you put x=-1/3 in the original eqn

Answer 76

wait so the local maximum is (4) at x= (1)
and the local minimum is (-4) at x= -1/3 ?

Answer 77

sorry wait I put -4 for maximum and 4 of minimum but it won't accept it

Answer 78

no, 4 has nothing to do with this...you just see whether the value is positive or negative...4 is positive..that means the corresponding value of x ( i.e. -1/3) that you plugged in to get 4 is the point of local minima...now plug -1/3 in the ORIGINAL eqn and find the value of the local minima

Answer 79

I got 8.81 is that right?

Answer 80

wait let me check

Answer 81

Yes..i think so..

the local minima would be 8.81 at x=-1/3

find out the local maxima and tell me..i'll verify that...after that we'll check the answer

Answer 82

got 10 for the Maxima

Answer 83

yes!..now am starting to pray again...please tell me that these answers are right..else i'll rest my case..._/\_

Answer 84

WINNERRRR! yep it worked

Answer 85

i can die in peace for the second time!

Answer 86

congrats Stacy and thanks

Answer 87

Haha well thank you again for everything Now i will be working on my Logarithims :/ haha

Answer 88

Thank you..don't thank me..you did all the work..:)