After today’s review of techniques for differentiation, try the questions listed below before our next class.
We’ve already seen how to find the equation of the tangent line to a curve that passes through a given point, and finding a normal through a given point on a curve is essentially the same. A normal is a line that is perpendicular to a tangent, and you will recall that if one line has slope \(m\), any line perpendicular to it will have slope \(-\frac{1}{m}\). For example, the equation of the line tangent to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has slope \(2\) (found by taking the derivative), and so has equation \(y=2x-1\). Similarly, the normal to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has equation \(y=-\frac{1}{2}x-1\).
Complete 16A questions 1acf, 2cd, and 4