Let $f:\rightarrow\mathbb{R}^{n-1}$ be a function such that $f\in\mathcal{C}^{\infty}(I)$. Evaluate the curvature of $\gamma(t):=(t,f(t))$ and prove that $\gamma$ is biregular if and only if $f''(t)\neq 0$, $\forall t\in I$.
I know that the curvature is
$$k(t):=\frac{\mid\mid\gamma '(t)\wedge\gamma '' (t)\mid\mid}{\mid\mid \gamma'(t)\mid\mid^{3}}.$$
But in this case I can't operate with this furmula and I don't know how to proceed. Can someone help me? Thanks before!