Calculus

# Intermediate Value Theorem

Between which of the following two values does the equation $-5x^4 + 7x^2 + 1=0$ have a solution?

Between which of the following two values does the equation $4x^3 + 7x - 13=0$ have a solution?

For the function $f(x)=2x,$ which of the following lies in the range of $f$ in the interval $[0, 1]?$

$f(x)$ is a continuous function on the interval $[25, 40]$. If $f(25) = 51$, $f(40) = 13$, and $f(a) = - 56$ where $25 < a < 40$, what are the least number of solutions to $f(x) = 0$?

Given the function $\displaystyle{f(x)=\frac{24x+8}{5x^2 - 15}},$ how many solutions does the equation $f(x)=0$ have on the domain $[-2, 2]?$

×