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Calculus

Differentiability

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 \([-2, 2]?\)

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