Question

Calculus. Help. :'(

Answer 1

for what non-negative valuof b is the line given by \[y=-\frac{ 1 }{ 3 }x+b\] perpendicular to the curve y=x^3?

Answer 2

take the derivative (with respect to x) of both equations , what do you get?

Answer 3

i got.. y'=-1/3+b and y'=3x^2 ..

Answer 4

waht do you do next?

Answer 5

try the derivative of the first equation again ( you made a mistake)

Answer 6

hm... i can't seem to find what my mistake was.. :/ is it the +b part??? because I do not know what to do with that...

Answer 7

b is really bx^0

Answer 8

so then, it would just be y'=-1/3???

Answer 9

thats better

Answer 10

so you have found the first derivatives of the those lines,

the first derivative is the slope of the line

Answer 11

the product of the slopes of perpendicular lines is -1

Answer 12

yes.. uhm.. give me a few min to think please :)

Answer 13

sure,

Answer 14

ah, i'm struggling.. please help

Answer 15

ok , so

\[m_1\times m_2=-1\]

\[m_1=-\frac13\qquad\qquad m_2=3x^2\]


solve for x

Answer 16

x=+1 or -1 .

Answer 17

good

Answer 18

now set \[y_1=y_2\]

take the first case (x=-1) and find b

Answer 19

does that make sense?

Answer 20

yes it does :) sorry. open study was being so slow .but i get it now. thank you! :)

Answer 21

what did you you get for an answer/

Answer 22

no what do i do..?