Question

The diagram shows the graph of the derivative of a function $f( x )$ for $0 \leq x \leq 4$ with $f(0)=0$. Which of the following could be correct statements for $y =f( x )$ ?

• A. Tangent line to $y =f( x )$ at $x =0$ makes an angle of $\sec ^{-1} \sqrt{5}$ with the $x$-axis.
• B. f is strictly increasing in $(0,3)$.
• C. $x =1$ is both an inflection point as well as point of local extremum.
• D. Number of critical point on $y =f( x )$ is two.

Answer 1

Answer: (A), (B), (D)

Slope of $y$ tangent at $x=0$ is $\tan ^{-1}(2) \Rightarrow( A )$ is correct
$f$ is obviously increasing for $(0,3)$
$\left(f^{\prime}( x ) \geq 0\right) \quad \Rightarrow$(B) is correct
$x =1$ being an inflection point
$x =1$ is inflection but not as extremum as $f^{\prime}( x )$ does not change sign hence (B) is not correct