How do you sketch the graph f(x)=x^3+1?

1 Answer
Tony B
Jul 5, 2016

see explanation

Explanation:

write as:" " y=x^3+1

At x=0; y=1 larr " y-intercept"
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(dy)/(dx)=3x^2 => "local max/min at "x=0 -> (0,1)

Only one x value for local max/min so the graph gradient goes from positive to 0 to positive again (no negative gradient)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

At y=0 => x^3=-1 larr" x-intercept"
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For 2 more points set x=+-2

At x=-2: x^3+1=-7-> (-2,-7)

At x=2: x^3+1 = +9->(+2,+9)

Tony B

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