main calculus sage page
You can plot a function and a secant line.
You can plot a function and secant lines tending toward a tangent line.
You can evaluate a derivative using its definition as a limit.
You can evaluate a derivative.
You can define a function, take its derivative, and plot both. Try changing to f(x)=(x-1)^2*sqrt(x) to see what happens. Then try f(x)=(x^5+x^3+2)/(8*x+1) ; change the interval to try to determine f'(0).
You can evaluate the derivative of a product with a manual product rule.
You can evaluate the derivative of a quotient with a manual quotient rule.
You can evaluate the derivative of a composition with a manual chain rule.
You can plot an implict curve $f(x,y)=0$. Try it for f(x,y)=2*y^3+y^2-y^5-x^4+2*x^3-x^2.
You can compute an implicit derivative.
You can evaluate a derivative involving exponentials, logs, hyperbolic functions, inverse trigonometric functions, ....
You can gather information to graph.
You can do Newton's method. Try setting p=0.5 and then p=3.0. Now try with f(x) = ((x-3/4)^(1/3))/(x^(1/3)) and p=0.1.
Last modified: Mon Mar 7 14:40:10 UTC 2022