A+ » VCE » Maths Methods U3 & 4 Master Notes » A3 Calculus » Local Maxima and Minima

# Local Maxima and Minima

## 5.5 Second Derivatives and Concavity

#### Second Derivatives and Point of Inflection

• The first derivative of a function is known as f^{\prime}(x). Similarly, we denote the second derivative of a function as f^{{\prime}{\prime}}(x) or \frac{d^2y}{dx^2}.
• If f^{{\prime}{\prime}}(x)>0 for an interval, the gradient of f(x) is increasing in the interval. The curve is said to be concave up (or have a ‘smiley face’)
Read More »5.5 Second Derivatives and Concavity