How do I write vertex as a maximum or minimum?
Question asks me to label the "vertex as a maximum or minimum"
The function is:f(x) = x^2+x-6
I found the vertex to be:
(-1/2,-25/4)
And it's at the bottom of the graph, not at the top so it would be minimum.
How do I use this information to answer this question?
Do I just say the vertex of the function is (-1/2,-25/4), which is the minimum of the graph?
Thanks!
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f(x) = x² + x - 6
or, f(x) = (x + 1/2)² - 25/4
Hence, vertex is at (-1/2, -25/4)
Now, as the coefficient of x² is positive, the function (parabola) will be ∪ - shaped
so, (-1/2, -25/4) is labelled as a minimum
A sketch is below.
:)>
If the term in 'x^2' is positive(+), then the vertex is a minimum; curve is bowl shaped.
If the term in 'x^2' is negative(-), then the curve is a maximum, curve is umbrella shaped.
You can doubly differentiate, then if the answer is positive/negative(+/-), then it is a minimum/maximum.
Hence
f'(x) = 2x + 1
f''(x) = (+)2 so it is a minimum.
If you look at the graph, there are NO values lower than -25/4, and all the rest are higher.
That's the definition of a minimum -- the lowest value in the given range (which can be a local minimum)