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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’)
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