The curves and intersect at and

MATHEMATICS · Single correct · GCSE · Mathematics · Algebra · Algebra

Problem

The curves

y=x^{2}

and

y=6x-x^{2}

intersect at

x=0

and

x=3

. On the open interval

(0,3)

, which statement is true? (a)

y=x^{2}

stays above

y=6x-x^{2}

throughout

(0,3)

. (b) They meet again at

x=\dfrac{3}{2}

inside

(0,3)

, so each curve is above the other on part of the interval. (c)

y=6x-x^{2}

stays above

y=x^{2}

throughout

(0,3)

. (d) The two curves coincide at every point of

(0,3)