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(x3+2x2-15x)
f'(x)= 1/8(3x2+4x-15)
=> quadratic formula to identify zero points of the first derivation.
x1/2=(-4+/-[math]16-4*3*(-15)[/math]) /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