Calculus

Differentiability

Intermediate Value Theorem

         

Between which of the following two values does the equation 5x4+7x2+1=0-5x^4 + 7x^2 + 1=0 have a solution?

Between which of the following two values does the equation 4x3+7x13=04x^3 + 7x - 13=0 have a solution?

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

f(x)f(x) is a continuous function on the interval [25,40][25, 40]. If f(25)=51f(25) = 51, f(40)=13f(40) = 13, and f(a)=56f(a) = - 56 where 25<a<4025 < a < 40, what are the least number of solutions to f(x)=0f(x) = 0?

Given the function f(x)=24x+85x215,\displaystyle{f(x)=\frac{24x+8}{5x^2 - 15}}, how many solutions does the equation f(x)=0f(x)=0 have on the domain [2,2]?[-2, 2]?

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