# Differentiation

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Again, that all makes sense. Thank you very much.

Thank you very much. I did get the derivative you show, but then divided through by 6 to get at the stationary points. Was that wrong?

given: f(x)= −2x 3 +21x 2 − 60x+17

1. Is 1st deriv of this -x^2+7x-10 ?

2. stationary points x=2; x=5 ?

3. these are a local min and a local max?

Thanks

1. No. It is -6 x^2 +42 x-60.
2. See if the derivative is zero at both points. If so, the answer is yes.
3. Look at the second derivative. Evaluate it at x=2 and x=5. If the signs are + and -, the answer is yea. These cannot be absolute maxima and minima points because f(x) goes to + and - infinity.

Dividing by 6 is OK when setting the derivative equal to zero. When the derivative is zero, so is 1/6 the derivative. Note that 1/6 of the derivative is -(x-2)(x-5), so you can see right away where the stationary points are.

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