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Why Function Is Not Differentiable?

Sophia Al-Mansoor • • 7 min read
Why Function Is Not Differentiable?

A function is not differentiable at a if its graph has a vertical tangent line

tangent line
In geometry, a tangent is a straight line that touches a curve at one point. At the place where they touch, the line and the curve both have the same slope (they are both "going in the same direction"). For this reason, a tangent line is a good approximation of the curve near that point.
at a. The tangent line to the curve becomes steeper as x approaches a until it becomes a vertical line. Since the slope of a vertical line is undefined, the function is not differentiable in this case.

How do you know if a function is not differentiable?

We can say that f is not differentiable for any value of x where a tangent cannot 'exist' or the tangent exists but is vertical (vertical line has undefined slope, hence undefined derivative).

What causes non differentiability in a function?

A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x.

Sophia Al-Mansoor
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Sophia Al-Mansoor

Sophia analyzes international trade, startup ecosystems, retail transformation, and supply chain logistics for modern digital publications.