IS \(\displaystyle{f{{\left({x}\right)}}}=-{2}{x}^{{{4}}}-{x}^{{{3}}}+{4}{x}+{4}\) concave or convex at

Efrain Watkins

Efrain Watkins

Answered question

2022-04-15

IS f(x)=2x4x3+4x+4 concave or convex at x=1?

Answer & Explanation

carlosegundoacyg

carlosegundoacyg

Beginner2022-04-16Added 10 answers

Step 1
Find the second derivative and then compute f(1). If the answer is positive, the graph is convex. If it's negative, the graph is concave at that point.
f(x)=8x33x2+4
f(x)=24x2+4
f(1)=24(1)26(1)=24+6=18
Since 18<0, the function is concave at x=1
Note: "concave" can also be called "concave downward" or "convex upward". It means the graph is heading downwards.

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