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Find e so that the graph of f(x) = c * x ^ 2 + x ^ - 2 has a point of inflection at (2, f(2)).

User Slattery
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1 Answer

7 votes

Answer:

Explanation:

First of all, I'm assuming we're finding c and not e.

Anyway, the inflection point is found where the second derivative is equal to 0. Therefore, if


f(x)=cx^2+x^(-2) , then


f'(x)=2cx-2x^{-3 and


f''(x)=2c+(6)/(x^4)

Now we'll evaluate that at an x value of 2, set the whole thing equal to 0, and solve for c:


0=2c+(6)/(16) which simplifies to


0=2c+(3)/(8) and


-(3)/(8)=2c so


c=-(3)/(16)

User Dejsa Cocan
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