Question

For the quartic function fx)=x^4-4x^3+8x+5, determine algebraically the:

c) coordinates of point M
d) areas of sections marked A, B, C and D
e) write the ratio of areas A:B:C:D in the form 1:b:c:d

Answer 1

Do you have the equation for line QM yet ?

Answer 2

yes I do.. I'm just not sure how to find the coordinates for M by applying the equation of the line QM?

Answer 3

Oh nice, its easy.
whats ur equation of line QM ?

Answer 4

y=-8x+21

Answer 5

nope, check again

Answer 6

Q = (0, 5)

right ?

Answer 7

oh I've got (2, 5) for the coordinates for Q

Answer 8

(2, 5) is the point R

Answer 9

solving for inflection points gives u :
http://www.wolframalpha.com/input/?i=%28x%5E4-4x%5E3%2B8x%2B5%29%27%27%3D0

Answer 10

0 and 2 are the x-coordinates of inflection points.

Since Q is to the left of R,
x coordinate of Q = 0, and x coordinate of R = 2

okay ?

Answer 11

that gives Q = (0, 5)
and slope = f'(0) = 8

so the equation of QM wud be : y-5 = 8x
or y = 8x+5

Answer 12

see if that looks okay...

Answer 13

thanks! i got the equation of the line QM now, but I was wondering how do I apply that to find out the coordinates of M?

Answer 14

solve both the equaitons simultaneously :

y =x^4-4x^3+8x+5
y = 8x+5

Answer 15

set the right hand sides equal and solve x

Answer 16

x^4-4x^3+8x+5 = 8x+5

x^4 - 4x^3 = 0

x = ?

Answer 17

awesome, thanks!

Answer 18

np :)

Answer 19

ssup ?

Answer 20

umm, sorry :P i was wondering about e).. do i just use the formula for the area of a semi circle for A, B and C? i'm not really sure about section D though?