$\textbf{Intermediate value theorem}$
Let $a<b$ be real numbers and $f:[a,b]\to\R$ a continuous function. Then for every $y_0$ between $f(a)$ and $f(b)$, i.e. $$\min(f(a),f(b))<y_0<\max(f(a),f(b)),$$there exists $x_0\in(a,b)$ such that $f(x_0)=y_0$.
$\textbf{Intermediate value theorem}$
Let $a<b$ be real numbers and $f:[a,b]\to\R$ a continuous function. Then for every $y_0$ between $f(a)$ and $f(b)$, i.e. $$\min(f(a),f(b))<y_0<\max(f(a),f(b)),$$there exists $x_0\in(a,b)$ such that $f(x_0)=y_0$.
copied
𝐈𝐧𝐭𝐞𝐫𝐦𝐞𝐝𝐢𝐚𝐭𝐞 𝐯𝐚𝐥𝐮𝐞 𝐭𝐡𝐞𝐨𝐫𝐞𝐦
Let 𝑎<𝑏 be real numbers and 𝑓:[𝑎,𝑏]→ℝ a continuous function. Then for every 𝑦₀ between 𝑓(𝑎) and 𝑓(𝑏), i.e.
min(𝑓(𝑎),𝑓(𝑏))<𝑦₀<max(𝑓(𝑎),𝑓(𝑏)),
there exists 𝑥₀∈(𝑎,𝑏) such that 𝑓(𝑥₀)=𝑦₀.