# User:Lena.kohl/curve sketching

# Curve Sketching

* exercise:*
curve sketching is the ability to design a graph with the facts you have been given in the original function. With it you can figure out it's first and second derivation ; zero points ;"mannerism ad infinitum" and the bending-behavior. That's what we show to you in the following example.

**original function:**

f(x)= 1/8(x^{3}+2x^{2}-15x)

f'(x)= 1/8(3x^{2}+4x-15)

=> **quadratic formula** to identify zero points of the first derivation.

x_{1/2}=(-4+/-[math]16-4*3*(-15)[/math]) /6

= (-4+/-14)/6

=> x_{1}= 5/3 x_{2}= -3

f"(x)= 1/8(6x+4)=> f"(5/3)= 1/8 (6(5/3)+4)= 7/4 => low point

f"(x)= 1/8 (6x+4) => f"(-3) = 1/8 (6*(-3)+4)= -7/4 => high point

**Mannerism ad infinitum:** f(x) from - to + , because x^{3} got an odd power of x

x->+/- infinitum

**y - value of the zero points from the first derivation :**

f(5/3)= 1/8 (3*(5/3)^{3}+2*(5/3)^{2}-15(5/3))= -0,69

f(-3)= 1/8 (3*(-3)^{3}+ 2*(-3)^{2}-15(-3))= - 2,25