Question

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

Answer 1

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)`