Which sign change of as passes through the critical value guarantees that the point…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Which sign change of

\dfrac{dy}{dx}

x

passes through the critical value

c

guarantees that the point

(c,\,y(c))

is a relative (local) maximum of

y

with respect to

x

? (a)

\dfrac{dy}{dx}

changes from negative to positive (b)

\dfrac{dy}{dx}

changes from positive to

0

(c)

\dfrac{dy}{dx}

changes from positive to negative (d)

\dfrac{dy}{dx}

is positive on both sides of

c