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(x3+2x2-15x)

f'(x)= 1/8(3x2+4x-15)

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

x1/2=(-4+/-$16-4*3*(-15)$) /6

= (-4+/-14)/6

=> x1= 5/3 x2= -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 x3 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