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If f(x)=2ax^3+x^2 and f'(x)=0 what is a?

1 Answer

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Answer:


x=-(1)/(3a)

Explanation:


f(x)=2ax^3 +x^2 \implies f'(x)=6ax^2 + 2x \\ \\ \therefore 6ax^2 + 2x=0 \\ \\ 2x(3ax+1)=0

Since f'(x)=0 for all x, we can ignore the case x=0.


3ax+1=0 \\ \\ 3ax=-1 \\ \\ x=-(1)/(3a)

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