Question

determine the intervals of increasing and decreasing, as well as all critical points for h(x)=x^4-4x^3+10. give the critical points in x-y coords.

Answer 1

http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtI.aspx This is a super duper tutorial on how to graph a function without using a calculator using 1st and 2nd derivatives. :)

Answer 2

h(x)=x^4-4x^3+10
h'(x)=4x^3-12x^2

set it = to 0 and solve

Answer 3

i got 3

Answer 4

it was after that step i don't know what to do

Answer 5

x=0,3

Answer 6

check x<0
check 0<x<3
check x>3

Answer 7

for x=-1
4x^3-12x^2
-4-12=-16
negative number
so function is decreasing x<0

Answer 8

-,-,+????

Answer 9

what?

Answer 10

you told me to check the values at the certain places and i got a -/-/+

Answer 11

dec/dec/inc.... would be another way of saying it

Answer 12

confirmed
http://www.wolframalpha.com/input/?i=Plot%5Bx%5E4-4x%5E3%2B10%2C%7Bx%2C-2%2C5%7D%5D

Answer 13

thank you for that... and the critical points would be 3 and 0? and i'm not sure how to give them in xy coords

Answer 14

(3,0) (0,0)

Answer 15

on that graph though... those aren't the spots they change concavity
or whatever else... its' more like (3,-3) (0,10)

Answer 16

by x,y coords, they mean x,h(x) coords i.e. y is just h(x) when you plot this function

Answer 17

so are the points 3,0 and 0,0

Answer 18

you want h(3) and h(0) for the second coord

Answer 19

thanks