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# Step maths-graphs watch

1. Had trouble with a question and looked at the solution.
Which I don't understand at all.

The solution says that since the curve has two stationary points, the quadratic obtained from differentiating it must have two distinct real roots. Could anyone shed any light on this?

The graph in question is ex(x-a)/(x-b)
Differentiates to x2-(a+b)x+(ab+a-b) = 0
and the discriminant is (a + b)2 - 4(ab + a - b) > 0
2. (Original post by Kvetch)
Had trouble with a question and looked at the solution.
Which I don't understand at all.

The solution says that since the curve has two stationary points, the quadratic obtained from differentiating it must have two distinct real roots. Could anyone shed any light on this?

The graph in question is ex(x-a)/(x-b)
Differentiates to x2-(a+b)x+(ab+a-b) = 0
and the discriminant is (a + b)2 - 4(ab + a - b) > 0
The root(s) of f'(x) is/are the x-value(s) of the point(s) where the curve is stationary.

Since there are two stationary points, there must be 2 such values, and hence real distinct roots, if it's a quadratic.

3. Thanks.
Wow, I feel dumb right now.
4. (Original post by Kvetch)
Thanks.
Wow, I feel dumb right now.
Lol - we've all had our Barbie moments.

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