Hello, Harry!
I agree with all your answers . . . Good work!
graph of f '(x) is attached.
is this correct:
f is increasing on (3,6) and (6,8)
f is concave down on (0,1.5) and (4.5,6) and (6,9)
the critical numbers of f are x=0, x=3, x=6, x=8
the values of x that f has a local maximum is x=8
the values of x that f has a local minimum is x=3
Good.f is increasing on (3,6) and (6,8)
Why only "9]" and not "10]"?f is concave down on (0,1.5) and (4.5,6) and (6,9)
No need to mention "convcave up"?
What's critical about x = 0 that is not critical about x = 10?the critical numbers of f are x=0, x=3, x=6, x=8
I'm always torn on this issue. Does "Local" include "Global"?the values of x that f has a local maximum is x=8
You may wish to ponder x = 0 on this one.
What do you think of x = 10?the values of x that f has a local minimum is x=3
aren't critical numbers where f '(x)=0?What's critical about x = 0 that is not critical about x = 10?
i think just "local"I'm always torn on this issue. Does "Local" include "Global"?
You may wish to ponder x = 0 on this one.
can endpoints be considered local maxima or local minima?What do you think of x = 10?
Hello, Harry!
First of all, I am guessing that consists of parabolic arcs.Does anyone know what the graph of would look like?
Do you really want to know? . . . You may be sorry you asked!
On the interval is a parabola through
. . Its equation is: .
Hence: .
On the interval is a parabola through
. . Its equation is: .
Hence: .
On the interval is a parabola through
. . Assuming (6,2) is the vertex, its equation is: .
Hence: .
We have a piecewise function: .
That definition is no good. The derivative has to exist in order for that to be sufficient.
What say you of x = 0 for f(x) = |x|? No derivative, but definitely a critical value.
Endpoints are the same. There is no derivative and they must be considered separately. Your text book or teacher should provide VERY CLEAR guidance on how to handle these situations.