(Solved): 1) Solve the points A, B and C step by step A) Apply the formal definition of derivative to find t ...

1) Solve the points A, B and C step by step A) Apply the formal definition of derivative to find the derivative of the following functions at the given point. \[ \begin{array}{l} f(x)=x^{3} \text { en } x=1 . \\ f(x)=\operatorname{sen}(x) \text { en } x=\pi \\ f(x)=4 x^{2}+5 x-4 \text { en } x=2 . \end{array} \] B) Find the equation of the tangent line to each curve at the indicated point. Check your answer by drawing the graph of the function and the graph of the tangent line. \[ \begin{array}{l} f(x)=x^{2}+1 \text { en } A(3, f(3)) \\ g(x)=\sqrt{x+1} \text { en } B(3, g(3)) \end{array} \] C) Find the derivative of the following functions. \[ \begin{array}{l} f(x)=\left(x^{2}+1\right)^{2} \\ f(x)=\left(x^{4}+3 x^{2}\right)\left(9-x^{2}+6 x-2\right) \\ f(x)=\frac{x^{5}}{x^{4}+x^{2}+1} \end{array} \]