Question

question 13suppose that $f(x)$ is a continuous function with the following values:| $x$ | 0 | 1 | 2 | 3 | 4 | 5 || --- | --- | --- | --- | --- | --- | --- || $f(x)$ | 6 | $-9$ | $-9$ | $-4$ | $-6$ | $-8$ |what is the minimum number of solutions to $f(x)=0$ in the interval $0 \leq x \leq 5$there are at least $square$ solutions.question help: $\blacktriangleright$ video $\boldsymbol{\boxplus}$ written examplesubmit question

Explanation:

Step1: Apply Intermediate Value Theorem (IVT)

Check sign changes of $f(x)$:

• At $x=0$, $f(0)=6$ (positive); at $x=1$, $f(1)=-9$ (negative). Sign change occurs, so at least 1 root in $(0,1)$.
• For $x=1$ to $x=4$, $f(x)$ stays negative; no sign change.
• At $x=4$, $f(4)=-6$ (negative); at $x=5$, $f(5)=-8$ (negative). No sign change.

Answer:

1