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Minimal value of an equation?

I don't think we've been taught what minimum values are but I'm doing this question:
Find the minimum values of 3x^3+12x+5

Can you please explain the steps? Thanks!
Original post by MelonKuma
I don't think we've been taught what minimum values are but I'm doing this question:
Find the minimum values of 3x^3+12x+5

Can you please explain the steps? Thanks!

The least possible value that y can take is the minimum.
To find this, you differentiate to find dydx\dfrac{dy}{dx} which you set as equal to 0. In the case that you have multiple possible values of x, then you substitute them into d2ydx2\dfrac{d^2y}{dx^2}. If d2ydx2<0\dfrac{d^2y}{dx^2}<0, then it's a maximum. The converse argument's for minimums.
(edited 10 years ago)
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davros
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Original post by MelonKuma
I don't think we've been taught what minimum values are but I'm doing this question:
Find the minimum values of 3x^3+12x+5

Can you please explain the steps? Thanks!


As keromedic says, you need to differentiate, and set the derivative equal to 0, then test the sign of the second derivative to see whether you have a minimum or a maximum.

Note that this method tells you about local maxima and minima - there is no such thing as the overall minimum of your function because as x gets more and more negative, so does your function :smile:

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