Let . Then which of the following alternative(s) is/are…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let f(x)=x+∫−1x(x−tx2)f(t) dtf(x) = x + \int_{-1}^x (x - tx^2)f(t)\,dt. Then which of the following alternative(s) is/are correct? (a) ff is continuous and derivable on RR (b) f′(−13)=1f'\left(-\frac{1}{3}\right) = 1 (c) maximum value of f(x)f(x) does not exist (d) lim⁡x→0f(x)=2\lim_{x \rightarrow 0} f(x) = 2

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