At which point on the curve does the tangent make an angle of with the positive -axis?

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

Problem

At which point on the curve

y=\sqrt{x}

does the tangent make an angle of

45^{\circ}

with the positive

x

-axis? (a)

\left(\dfrac{1}{2},\dfrac{1}{\sqrt{2}}\right)

(b)

\left(\dfrac{1}{4},\dfrac{1}{2}\right)

(c)

\left(\dfrac{1}{2},\dfrac{1}{4}\right)

(d)

\left(\dfrac{1}{16},\dfrac{1}{4}\right)