S.O.S. Mathematics CyberBoard

[Kashif]

Find the coordinates of the stationary point on the curve:

y=3^2x - 18 (3^x)

Thanks.

[Kwyjibo]

Hello, Kashif!

The stationary, or critical points of a function occur when the derivative
is zero. So let's set your derivative equal to zero and solve for x!


.

.



.

Here you can see that the only x value that makes this expression true
is 2, because when x gets larger than 2 the left side of this equation gets
larger then the right, and when x is less than 2, the right side is larger.

So our critical point is at x=2.

Now we plug this into our function, to obtain the y value.



So the critical point is at (2,-81).

You could use the first and second derivative tests to determine if this is
a maximum or minimum, but you should be asble to easily convince
yourself that it is a minimum.

-Kwyjibo
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