Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

How do you find and classify the critical points of this differential equation #dx/dt = 2x + 4y + 4#?

Answer 1

Elijah Abram

Critical Points occur when the first derivative vanishes, ie when #(dx)/(dt)=0# which requires that

# 2x+4y + 4 = 0 #

ie along the curve #x+2y+2=0#

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Answer 2

Ezra Adams

To find and classify the critical points of the differential equation ( \frac{dx}{dt} = 2x + 4y + 4 ), we need to set the equation equal to zero and solve for ( x ) and ( y ).

Given: ( \frac{dx}{dt} = 2x + 4y + 4 )

Setting ( \frac{dx}{dt} = 0 ), we have:

[ 2x + 4y + 4 = 0 ]

Now, to classify the critical points, we'll need additional information about ( y ). Without that, we can't fully classify the critical points. We'd need another equation involving ( y ) to proceed further. If you have such an equation, we can incorporate it to find the critical points and classify them accordingly.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.