Question

State whether the following statement is true or false.

Enter $1$ for true and $0$ for false

$f\left(x\right)$ is differentiable at a point $P$, if there exists a unique tangent at point $P$.

Answer 1

The function $f\left(x\right)$ is differentiable at a point $P$, if and only if there exists a unique tangent at point $P$. In other words, $f\left(x\right)$ is differentiable at point $P$, if and only if the curve does not have $P$ as the corner point i.e. the function is not differentiable at those points on which the function has sharp edges.