The one-sided limits of the derivative of a continuous function at are _ x 2^-…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The one-sided limits of the derivative of a continuous function

f

x=2

are

\lim_{x\to2^-}f'(x)=-3,\qquad \lim_{x\to2^+}f'(x)=5.

Which of the following is most consistent with the behavior of

f

x=2

? (a)

f

has a vertical tangent line at

x=2

. (b)

f

has a sharp corner at

x=2

. (c)

f

has a removable discontinuity at

x=2

. (d)

f

has a local extremum at

x=2