Question

Hello am new here need ur help..
For the function f(x)=2xcube-7xsquare+4x+1
a) Find the instanteneous rate of change at x=0 and x=1
b) Is the function increasing or decreasing at x=0? how about at x=1?
c) Do you expect a local miximum or local minimum when 0 14 years ago

Answer 1

yeah i got stock with x=0

Answer 2

\[f(x)=2x^3-7x^2+4x+1\]and that is not the formula for instantaneous rate of change above

Answer 3

instantaneous rate of change is found through taking the derivative

Answer 4

Just find f'(x) and sub in the x values

Answer 5

Oh. That's true. Sorry. That's the average rate of change.

Answer 6

so @khally92 what did you get for the derivative?

Answer 7

6xsquare-14x+4

Answer 8

and so what did you get for f'(1) and f'(0) ???

Answer 9

f(1)= -4 and f(0)=4

Answer 10

and those are the answers for a)
nice job :)
to answer part b) we just need to remember that
f(x) is decreasing is when f'<0
f(x) is increasing is when f'>0
so what is the answer to that part?

Answer 11

f>0 so that means its increase and at x=1 is decreasing

Answer 12

at -4 is decreasing and at 4 is increasing.. hello

Answer 13

sorry
at x=1, f'<0 so it's decreasing yes

Answer 14

an yes to the other question too
now what do you think about part c)

Answer 15

no graph to conclude whether 0<x<1 is a local mini or local maxi

Answer 16

Put f'(x)=0 Find the turning point within the range. Then find the 2nd derivative and sub that value in. If <0 then max, if >0 min.

Answer 17

You can use your answer to part b. If it is increasing first then decreasing, then max. If it is the other way round then min.

Answer 18

its increasing decreasing so its a local max ryt?

Answer 19

Yes, if that is the case

Answer 20

yes... thank you thank you very much n @turningpoint too thnks alot

Answer 21

TuringTest=Turningpoint :D

Answer 22

another one please differentiate f(x)= squareroot of x-square of 3. can u please write it out let me see if its correct

Answer 23

Is this what the equation looks like x^(3)^(1/2)^(1/2)? ^(1/2) is the same as squaring. Just use exponent rules and simplify to get (1/2)*(1/2)*3 = 3/4 so x^(3/4) then differentiate that as you normally would using nx^n-1. Know what I mean?

Answer 24

yeah i know that power rule is that what am going to use.. this is the question again squareroot of x - squareroot sign3outside then x inside hope u gog the equation ryt.. i got 1/2suare root of x-1/3square root of x is tha correct

Answer 25

can you use numbers and ^ for to the power I cannot understand what you are trying to show

Answer 26

well here is the equation xraisedpower of 1/2 - xraised power of -1/3... hope that helps

Answer 27

Yeah I can understand that a little better it just isnt a very good way of writing the question. You just use power rule. Do you know how to subtract from a fraction? Post your answer I will tell you if it is correct.

Answer 28

x raisedpower of -1/2 divide by2 - xraised power of -2/3 divide by 3. which i can futher simplyfy

Answer 29

thank you...

Answer 30

No problem you solved it.

Answer 31

Last for the day the mass mass of M in gramms of undissolved sugar left in a tea cup after t seconds is given by M=10.5-o.4tsquare. when will the sugar dissolve?

Answer 32

You are looking for the time when mass is equal to zero so what do you think you should set your mass to in your equation?

Answer 33

looking fo time when mass is zero...so i should find a value for t that will make m zero?e m zero?

Answer 34

Yes and inorder to find the t that make m=0 you just set M to 0 in the equation and then solve for t.

Answer 35

thats squareroot of 26.25

Answer 36

Correct.

Answer 37

Back to differenciation 3x/x2+4... am going to use the product rule ryt when x2+4comes up having the negative sign could u please help me differenciate the (x2+4)-1..

Answer 38

okay easy you will also need chain rule. Just do 3x*(x^2+4)^-1 like you said and use product rule to get 3x'*(x^2+4)^-1+3x*(x^2+4)^-1' try it yourself and I will help you from there.

Answer 39

well thats (3x)(2x)^-1 + (3)(x^2+4)

Answer 40

Okay lets back up.

Answer 41

well thats (3x)(2x)^-1 + (3)(x^2+4)^-1

Answer 42

Okay it seems like you understand the product rule but not the chain rule. for (x^2+4)^-1 first you take the derivatie of the outside then you multiply that by the derivative of the inside understand?

Answer 43

thats-1x

Answer 44

Okay here I will help you (-1)(x^2+4)^-2*(2x) do you understand how I did this?

Answer 45

yeah i do kind of look loke caine rule

Answer 46

It is the chain rule haha.

Answer 47

you want to show the whole problem solved to see if you got it or do you feel confident you have it?

Answer 48

Find the equation of the tangent to y=x2-3x-4 is parrelto the line y=7x+3..... i jus need to know if the answer i got is correct. i have y=7x-29 points on the curve arex=5 and y=6 are the answers correct. good evening

Answer 49

yes you got it