## 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

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### 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

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