Question

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

Answer 1

see explanation

Explanation:

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

At `x=0; y=1 larr " y-intercept"`
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`(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)
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At `y=0 => x^3=-1 larr" x-intercept"`
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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)`