#inflection points

In a world where busyness often masquerades as progress, Matt Spielman’s Inflection Points: How to Work and Live with Purpose offers a refreshing, actionable roadmap for reclaiming intentionality, fulfillment, and clarity. This isn’t just another self-help book—it’s a strategic life manual and transformative guide to redefining success on our own terms. More than just another self-help book, Inflection Points is a deeply human, introspective journey into the moments that shape our lives—both professionally and personally. With a blend of personal anecdotes, psychological insights, and practical frameworks, Spielman invites readers to pause, reflect, and realign their lives with purpose. More details…

Should You Expand Your Business to a New Market?

Diversify or die. Pivot or persevere. These are the adages that accompany expanding into new markets. And they are harrowing to entrepreneurs, to say the least.

“Don’t do it and you’ll fail” — that’s what they mean. But in the startup world, expanding is a double-edged sword. If you diversify too soon, you will also fail.

New markets are alluring. They shine with possibility. They glisten with a…

Like the first derivative of a function, the second derivative of a function provides useful information about the shape of the graph. It determines whether the graph is bending upward with an increasing slope or downwards with a decreasing slope.

Concavity Definition If f''(x) > 0 on interval I, then f is concave up on I. if f''(x) < 0 on interval I, then f is concave down on I.

Concavity is defined for only differentiable functions.

Some observations can be made from the graph about concavity. 1. If f is concave up on an interval, then its tangent lines lies below the graph of the function and its secant lines lie above the graph of the function. 2. If f is concave down on an interval, then its tangent lines lies above the graph of the function and its secant lines lie below the graph of the function. 3. If the graph of f has a tangent line at a point, b, and if concavity of f is opposite on opposite sides of that point, then the graph crosses that tangent line at that point, b, changing the concavity of the graph at point b, where b is called the inflection point.

Inflection Points Definition A point, x₀, is called an inflection point of f if the following is true: 1. The graph of y = f(x) has a tangent line at x₀. 2. The concavity of f is opposite on each side of x₀.

The Second Derivative Test A function f will have a loc max, or loc min, value at a critical point if its graph is concave downward, or upward, nearby.

Now that I have a lot more space, I’m at a definite fork in the road w/r/t collecting/salvaging stuff. And making stuff out of some of that stuff, and making other stuff.

Fork One: keep amassing, and making, for the joy it brings me. AKA, become the H-word. (NO WAY I’M NOT THROWING OUT THAT CRUSTY PIECE OF RUSTED SHEET METAL; IT HAS PERFECT COLORATION AND WILL BE AN AMAZING SIGN CANVAS. IT’S MY PRECIOUS DON’T TOUCH IT I’LL CUT YOU.)

Fork Two: Have a go at selling my treasures as a bona fide (HEY WHO JUST LAUGHED) side career. I’m taking baby steps toward this, although it’s maybe one step forward/two steps back, because each time I think about selling any fucking thing, I might as well have Al Swearengen plunging a Bowie knife into my spleen/small colon area. (Oh, the painless siren song of Fork One.)