For what values of x is \(\displaystyle{f{{\left({x}\right)}}}={\left({x}-{2}\right)}{\left({x}-{4}\right)}{\left({x}-{3}\right)}\)

Aliana Alvarez

Aliana Alvarez

Answered question

2022-04-13

For what values of x is f(x)=(x2)(x4)(x3) concave or convex?

Answer & Explanation

unduncjineei5r3

unduncjineei5r3

Beginner2022-04-14Added 19 answers

Step 1
To find where a function is concave or convex, find where f(x) is positive or negative (respectively).
f(x)=(x2)(x4)(x3)
f(x)=(1)(x4)(x3)+(x2)(1)(x3)+(x2)(x4)(1)
f(x)=x27x12+x25x+6+x26x+8
f(x)=3x218x+2
f(x)=6x18
f(x)=6(x3)
f(x) is negative from (, 3), and positive from (3, )
Therefore, f(x) is concave on (, 3), and convex on (3, )

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