Four smooth curves , ,

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Four smooth curves

W

X

Y

, and

Z

are defined for

x>0

W(x)=\sqrt{x}

X(x)=\frac{1}{2\sqrt{x}}

Y(x)=-\frac{1}{4}x^{-3/2}

Z(x)=\ln x

. Exactly three of these curves constitute the set {

f

f'

f''

} for some twice-differentiable function

f

. Determine which three curves belong to that set and label each as

f

f'

, or

f''