Question

Give the correct order of initials $T$ or $F$ for following statements. Use $T$ if statement is true and $F$ if it is false.
Statement-1: If $f:R\to R$ and $c\in R$ is such that $f$ is increasing in $(c-\delta ,c)$ and $f$ is decreasing in $(c,c+\delta )$ then $f$ has a local maximum at $c$. Where $\delta$ is a sufficiently small positive quantity.
Statement-2 : Let $f:(a,b)\to R,c\in (a,b)$. Then $f$ can not have both a local maximum and a point of
inflection at $x=c$.
Statement-3: The function $f(x)=x^2|x|$ is twice differentiable at $x=0$.
Statement-4 : Let $f:[c-1,c+1]\to [a,b]$ be bijective map such that $f$ is differentiable at $c$ then $f^{-1}$ is also differentiable at $f(c)$.

• A. FFTF
• B. TTFT
• C. FTTF
• D. TTTF

Answer 1

Answer: (C)

S-1 : f must be continuous $\Rightarrow$ false $S-2x=c$ is local max.but not inflection point $\Rightarrow$ True