Is \(\displaystyle{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}-{2}\right)}-{x}^{{2}}+{x}^{{3}}\) concave or convex at

Abbey Ellison

Abbey Ellison

Answered question

2022-04-16

Is f(x)=(x3)(x2)x2+x3 concave or convex at x=1?

Answer & Explanation

Drantumcem0

Drantumcem0

Beginner2022-04-17Added 10 answers

Step 1
To determine if a function is concave up or down at a point, you need to examine the sign of the second derivative f"(x) at that point.
First, multiply out and simplify f(x):
f(x)=x22x3x+6x2+x3
f(x)=x35x+6
Step 2
Find f'(x) and then f"(x):
f(x)=3x25
fx)=6x
At x=1,f1)=6<0. Since the second derivative is negative at x=1, that indicates that the method is concave down.

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