Question

If for a function $f\left(x\right),f^{\prime }\left(a\right)=0,f^{\prime \prime }\left(a\right)=0,f^{\prime \prime \prime }\left(a\right)>0$, then at $x=a,f\left(x\right)$ has which of the following?

• A. Minimum
• B. Maximum
• C. Not an extreme point
• D. Extreme point

Answer 1

The correct option is C Not an extreme point

If for the function f(x) we have $f^{\prime }\left(a\right)=0$ means that 'a' is a critical point of the function but $f^{\prime \prime }\left(a\right)=0$ means the function has neither a maxima or minima at that point. Hence the function has no extreme point at x =a as concavity of the curve does not change due to absence of a maxima or minima at the point x =a Hence option C is correct