Differentiable vs ContinuousOne implies the other, in exactly one direction.MathematicsContinuous at alim f(x) = f(a) as x approaches aNo jump, no hole, no blow-upRequires no tangent line|x| is continuous everywhereThe weaker conditionDifferentiable at aThe difference quotient has alimitA unique tangent line existsImplies continuity at a|x| fails this at x = 0The stronger conditionTHE DIFFERENCE THAT MATTERSDifferentiable implies continuous. The converse is false, andspectacularly so.The Weierstrass function is continuous everywhere and differentiablenowhere. Continuity buys far less than intuition suggests.Differentiable vs Continuouslearnposters.com
Differentiable vs Continuous — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Differentiable vs Continuous poster

Continuous at a against Differentiable at a, side by side.

The Weierstrass function is continuous everywhere and differentiable nowhere. Continuity buys far less than intuition suggests.

Questions about the Differentiable vs Continuous poster

What’s on the Differentiable vs Continuous poster?
Continuous at a against Differentiable at a, side by side. Continuous at a: lim f(x) = f(a) as x approaches a; Continuous at a: No jump, no hole, no blow-up; Continuous at a: Requires no tangent line; Continuous at a: |x| is continuous everywhere; Continuous at a: The weaker condition; Differentiable at a: The difference quotient has a limit; Differentiable at a: A unique tangent line exists; Differentiable at a: Implies continuity at a; Differentiable at a: |x| fails this at x = 0; Differentiable at a: The stronger condition; Differentiable implies continuous. The converse is false, and spectacularly so.. The Weierstrass function is continuous everywhere and differentiable nowhere. Continuity buys far less than intuition suggests.
Who is the Differentiable vs Continuous poster for?
Differentiable vs Continuous belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning analysis can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Differentiable vs Continuous poster?
Whenever a proof needs a derivative and only continuity has been assumed. A wall chart earns its place by being glanceable from where the work is happening, so Differentiable vs Continuous belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Differentiable vs Continuous?
Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Differentiable vs Continuous in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Absolute vs ConditionalBolzano-WeierstrassCauchy Sequences
Is the Differentiable vs Continuous poster free to download and print?
Yes. Differentiable vs Continuous downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Differentiable vs Continuous poster print at?
Differentiable vs Continuous is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Differentiable vs Continuous loses nothing.Printing guide

Related posters

Charts that sit alongside Differentiable vs Continuous on the same wall.

Browse every Mathematics poster, or start from the full catalogue.