Curve Sketching 

1. The graph of \(y=f(x)\) is given below. Find the interval(s) where (a) \(f'> 0 \), \(f'< 0 \), \(f''> 0 \) and \(f'' < 0 \), (b) Relative max/min of \(f\), and (c) Inflection points of \( f \).   solution

2. Sketch a function \(f(x)\) that satisfies the following conditions.  solution

(a) \(f'(x) >0, \: f''(x)>0\ \) on \((-\infty, -2)\).

(b) \(f'(x) >0, \: f''(x)< 0 \) on \( (-2, \infty)\).

3.If \( y =f(x) \) is a continuous function such that \(f'<0\) and \(f''>0\) for all \(x\). Which of the following could be graph of the function of \(y=f(x) ? \) solution