Calculus Extrema of Functions Help

[keen cave]

Could somebody help me with this?

[fallen totem]

for d. x=5 isnt a local min since values like x=5-(small number) have smaller function values

[keen cave]

what do you mean?

[fallen totem]

You put [5,7] in part d, but x = 5 is not a local min, so it should be (5,7]. Just look at the function values slightly less than x=5 and notice it will always be smaller than f(5).

More formally:

If a point "x" is a local minimum, then you should be able to find some interval around the point, (x-a,x+a), such that whenever you take a point "y" in this interval, f(y) >= f(x).

For x=5 no matter what interval (x-a,x+a) you take, you can choose y = x - (a/2), and for this point f(y) < f(x), thus its not a local minimum.

[keen cave]

Oh okay thank you, but for c.) I would keep my answer [5, 7]?