Second Order Derivatives
Second order derivatives
- You can get second order derivatives by differentiating twice (aka. differentiating the gradient function of your original function)
- This can be used to find acceleration from displacement, as acceleration is metres per second, per second.
If \(y=5x^3-\frac{x}{3\sqrt{ x }}\), find the second derivative.
- \(y=5x^3-\frac{x}{3\sqrt{ x }}\)
- \(y=15x^2-\frac{1}{6}x^{\frac{1}{2}}\)
- \(y=30x+\frac{1}{12}x^{\frac{3}{2}}\)
Find the least value of \(f(x)=x^2-4x+9\)
- Differentiate:
- \(f^{'}(x)=2x-4=0\)
- \(x=2\)
- \(f(2)=2^2-4(2)+9=5\)
- \(y=5\) is the minimum value.