Thread: Hi i need help with a two part function and symmetry problem

1. Hi i need help with a two part function and symmetry problem

Hi, i have a two part symmetry and function related question:
A. Find the point of symmetry of the graph of the cubic function:
f(x)=-x^3+15x^2-48x+45

B. The function has a local minimum at (2,1). At what point does a local maximum occur?
I don't understand how to go about this problem.. can anyone help?

2. Originally Posted by mathstudent123
Hi, i have a two part symmetry and function related question:
A. Find the point of symmetry of the graph of the cubic function:
f(x)=-x^3+15x^2-48x+45

B. The function has a local minimum at (2,1). At what point does a local maximum occur?
I don't understand how to go about this problem.. can anyone help?
1. With a cubic function the point of symmetry is the inflection point. Therefore solve for x:

f''(x) = 0

2. The point of symmetry is the midpoint between 2 corresponding points of the graph. If the point of symmetry is S(5, 55) and the maximum point is M(a, b) then

$\dfrac{2+a}2 = 5~\wedge~\dfrac{1+b}2=55$