Question

Let the tangent to the graph of $y=f\left(x\right)$ at the point $x=a$ be parallel to the x-axis,and let $f^{\prime }(a-h)>0$ and $f^{\prime }(a+h)<0$,where h is a very small positive number.Then the ordinate of the point is

• A. a maximum
• B. a minimum
• C. both a maximum and minimum
• D. neither a maximum nor a minimum

Answer 1

The correct option is A a maximum

Tangent is parallel to x axis
$\Rightarrow y^{{}^{\prime }}=f^{{}^{\prime }}\left(a\right)=0$
And $f(x-a)>0,f(x+a)<0$ gives $x=a$ is point of maxima
Hence, option 'A' is correct.