Statement I *The function is an odd function and is an even function.* Statement II…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Statement I *The function f(x)=∫0x1+t2dtf(x) = \int_{0}^{x} \sqrt{1+t^2} dt is an odd function and g(x)=f′(x)g(x) = f'(x) is an even function.* Statement II *For a differentiable function f(x)f(x) if f′(x)f'(x) is an even function, then f(x)f(x) is an odd function.*

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