Statement I The equation has atleast one solution in

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Statement I The equation x34−sin⁡πx+23=0\frac{x^3}{4} - \sin \pi x + \frac{2}{3} = 0 has atleast one solution in [−2,2][-2, 2] . Statement II Let f:[a,b]→Rf: [a, b] \to R be a function and cc be a number such that f(a)<c<f(b)f(a) < c < f(b) , then there is atleast one number n∈(a,b)n \in (a, b) such that f(n)=cf(n) = c .

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