For a positive constant

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For a positive constant tt, define Ft(x)=etx−x−2F_t(x)=e^{tx}-x-2 on the interval [0,1][0,1]. For which of the following conditions on tt is it guaranteed that the equation etx=x+2e^{tx}=x+2 has at least one solution with xx in (0,1)(0,1)? (a) 0<t<ln⁡30<t<\ln 3 (b) t=ln⁡3t=\ln 3 (c) t>ln⁡3t>\ln 3 (d) ln⁡2<t<ln⁡3\ln 2<t<\ln 3

Related theory

Browse the problem library