For all real

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For all real xx, three functions are defined by F(x)=4sin⁡x(x)=4\sin x, G(x)=4cos⁡x(x)=4\cos x, H(x)=−4sin⁡x(x)=-4\sin x. Exactly one of these functions is a twice-differentiable function ff, and the other two are its first and second derivatives. Which of the following identifications is correct? (a) G is ff, H is f′f', F is f′′f'' (b) F is ff, G is f′f', H is f′′f'' (c) G is ff, F is f′f', H is f′′f'' (d) F is ff, H is f′f', G is f′′f''

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