# calculus ..>steve

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Given a function
f(x)2/3x^3+5/2x^2-3x.

a) Find

i. The inflection point.
ii. The y-intercept and x-intercept.

b) Sketch the graph of f(x).

i have already try it..but i don't understand.. which graph that is true.. the first or second ? and how to calculate the x,y intercept,and inflection point? i hope you can help me to solve this ..

• calculus ..>steve -

y = 2/3 x^3 + 5/2 x^2 - 3x
y' = 2x^2 + 5x - 3
y'' = 4x + 5

inflection where y''=0 -- at x=-5/4
intercepts at (0,0)
and at x = 3/8 (-5±√57)

Looks like you need to review the meanings of 1st and second derivatives.

• calculus ..>steve -

remember that the first derivative gives you the max's and min's and the second derivative tells you concavity and inflection points

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