Math SL Seniors- Calculus

This week we started the introduction to our Calculus unit and began with a question that we would later answer by learning the material. Can a function that is not a straight line have a slope? We later answered this by saying that we could draw a tangent line to the curve which would give us the slope. The next thing that was puzzling involved the accuracy of the slope that the tangent line would give us yet realized that the closer two points are on a curve, the more accurate the slope would be at the specific point in time, the instantaneous slope. The derivative function is what gives us the gradient of f(x) at a point, x, in the domain. We learned how to differentiate from 1st Principles by using the formula on our sheet that includes the limit as “h” approaches zero. The most important thing thus far is ALGEBRA. You need to complete the question algebraically before attempting to find the derivatives. It will make life a lot easier!! Then came the Power Rule, which is a shorter way to differentiate rather than the tedious formula on our sheet. You multiply the coefficient by its exponent and then subtract the exponent by 1. Lastly, we learned the Chain Rule which basically says that the derivative equals the outside times the inside. The outside is: bringing the exponent in front of the equation as a coefficient, bringing down the original equation to put in parentheses after that coefficient and then its exponent is one less than its original form. This outside is multiplied by the inside which is: the derivative of the equation given. So far, Calculus is going great as long as you can remember the simple algebra rules :)