Mathematics

Mathematics

Problem

Which sign change of

\dfrac{dy}{dx}

as

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

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