Question

@DanJS

Answer 1

yep exactly this is what i meant by practice. lol

Answer 2

well this one is only a practice test which doesnst count for anything, i just like learning it a bit cause alot of the questions are like similar, and you explain it really well

Answer 3

a little trick that can help you get started...

Answer 4

when you take the derivative of a polynomial, what happens to the highest power in the polynomial?

Answer 5

d/dx ( x^n) = n*x^(n-1)

the power is decreased by 1, when you take the derivative

Answer 6

right?

Answer 7

\[\frac{ d }{ dx }[3x^4 + 4x^2] = 12x^3 + 8x\]

the degree (highest power of the polynomial decreases by 1

Answer 8

when you have a polynomial , say to the 4th power, it will have 4 roots where it crosses the x axis

Answer 9

Purple Line - 4 times
Red Line - 3 times
Blue Line - 2 time

Answer 10

so the purple line is f(x)
red f ' (x)
bluef '' (x)

Answer 11

you see the number of times they cross the x axis reduces by 1 each time,

Answer 12

you see what i mean?

Answer 13

A would be f' right?

Answer 14

Purple line crosses x axis 4 time... it is a 4th degree polynomial
something like

f(x) = x^4

Answer 15

if you take the derivative of f(x) = x^4 you get

f ' (x) = 4x^3 the degree is now 3, it will cross the x-axis 3 times

Answer 16

each time you take a derivative of a polynomial, it will cross the x axis 1 less times

Answer 17

so A is f '' (x)

Answer 18

B is f (x)

Answer 19

C is f ' (x)

Answer 20

ohh this isnt a hard question at all

Answer 21

no, that is just a little trick for polynomials

Answer 22

the roots reduce by one each derivative, crosses the x axis 1 less times each derivative taken

Answer 23

can i list another question and do it and see if i got it right?

Answer 24

but look at the features here....

Answer 25

When the purple line of f has a horizontal tangent line, the red graph of f '(x) should go through x = 0,

Answer 26

like at x = 0, the purple line has a horizontal tangent, and the red line goes through y = 0

the rate of change of the purple line is zero, and the graph of the rate of change, the red line, goes through y = 0

Answer 27

got it!

Answer 28

any time you have a round shape where concavity changes , the derivative has to go through y = 0, cross the x axis