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.

x_1/2=(-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

sketch

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