Mathegoras

Calculus › Extrema and curve sketching › Bounds from derivatives

Minimum roots of g times g'

University · ●●●○○ 50 pts

Let ff be a function defined for all x∈Rx \in \mathbb{R} that is discontinuous at exactly 33 values of xx. Let gg be a differentiable function such that f(x)g(x)f(x)g(x) is continuous for all x∈Rx \in \mathbb{R}. Find the minimum number of distinct real roots of the equation g(x)g′(x)=0g(x)g'(x)=0.

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continuitylimitsRolle's theorempolynomial rootsderivatives