function has a corner?

Question

what does it mean if f(x) has a corner at x = a?
what does the graph look like?

Answer 1

Are you looking for a calculus answer?

For a continuous function f(x) defined on an interval, if there is a point "a" in that interval, such that the limit as f' approaches a from the right is not equal to the limit as f' approaches from the left, then you can say that the function has a "corner".

One consequence that falls out immediately, is that the derrivative function f' is discontinuous at a.

Two examples would be:

f(x)= |x| this is a V shaped graph that slopes up away from the x axis both in the +x and -x directions. For values of x<1 the slope is -1, and f'(x) = -1. For values of x>1 the slope is 1, and f'(x) = 1. f'(x) is therefore not defined at x=0, and the derrivative function is discontinuous.

Another example would be something like:

f(x)=0 for values of x< or = to 0
f(x)=x for values of x>0

This function is defined differently over two portions of the domain, but the graph is continuous. The derrivative is 0 for the first part and 1 for the second. The derrivative is undefined for x=0.

.... Hope that helps!

Answer 2

It looks just like a corner. Mathematically, a corner occurs when the right and limits are not equal, but neither are positive or negative infinity (that would be a cusp or a vertical tangent)

Answer 3

Symbolic fairly than something else - you'll in basic terms punch hrough the walls in case you've been minded to attack. They ensue in distinct tiered pagoda platforms and are effortless throughout Asia - and probably serve a more convenient funtion of controlling rainwater run-off contained in the absence of gutters.

Answer 4

This means that f(a) is last or beginning of the function