Tutorial 2 - Calculus, Plotting, Interact.ipynb

Kernel: SageMath (stable)

%html

Calculus, plotting & interact

Exercise: Let $f(x) = x^4 + x^3 - 13 x^2 - x + 12$. Define $f$ as a symbolic function.

%html

 

Exercise: Plot $f$ on the domain $-4.5 \leq x \leq 3.5$.

%html

 

Exercise: Find numerical approximations for the critical values of $f$ by taking the derivative of $f$ and using the find_root method. (Hint: plot the derivative.)

%html

 

Exercise: Find numerical approximations for the critical values of $f$ by taking the derivative of $f$ and using the roots(ring=RR) method. (Here, RR stands for the real numbers.) Are there any roots over the ring of rationals (QQ)?

%html

Exercise: Compute the equation $y = mx +b$ of the tangent line to the function $f$ at the points $x=-1$ and $x=2$.

%html

Exercise: Write a function that takes $x$ as an argument and returns the equation of the tangent line to $f$ through the point $x$.

%html

Exercise: Write a function that takes $x$ as an argument and plots $f$ together with the the tangent line to $f$ through the point $x$. Make the line red.

%html

Exercise: Convert the function you created above into an @interact object. Turn the argument $x$ into a slider. (Hint: see the documentation for interact for examples on creating sliders.)