To calculate: \(\displaystyle{f{{\left({x}\right)}}}=-{3}{x}^{{{5}}}-{2}{x}^{{{4}}}-{6}{x}^{{{3}}}+{x}-{7}\) concave or convex at

Colt Rhodes

Colt Rhodes

Answered question


To calculate:
f(x)=3x52x46x3+x7 concave or convex at x=5?

Answer & Explanation



Beginner2022-04-11Added 8 answers

Step 1
It's a pretty straightforward polynomial, so taking the derivative is pretty easy. You can just derive the terms one by one, proceeding left to right:
And then, do it again:
You can plug in x=5 and calculate if you want, but if you're pressed for time on an exam it's not really necessary. Each term in the second derivative is negative for x=5, so the second derivative is therefore negative at that point, so it's convex (or concave downward) at x=5.

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