Waste less time on Facebook — follow Brilliant.
×

Differentiability

Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.

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 \([-2, 2]?\)

×

Problem Loading...

Note Loading...

Set Loading...