How do you find the inflection point, concave

Christopher Stone

Christopher Stone

Answered question

2022-04-16

How do you find the inflection point, concave up and down for f(x)=x33x2+3?

Answer & Explanation

annie996k88v

annie996k88v

Beginner2022-04-17Added 11 answers

Step 1
The first derivative is f(x)=3x26x and the second derivative is fx)=6x6=6(x1). The second derivative is negative when x<1, positive when x>1, and zero when x=1 (and of course changes sign as x increases "through" x=1).
Step 2
That means the graph of f is concave down when x<1, concave up when x>1, and has an inflection point at x=1. The coordinates of the inflection point are (x,y)=(1,f(1))=(1,1).

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