SOLUTION: 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
Algebra.Com
Question 222059: 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.. help?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A. Find the point of symmetry of the graph of the cubic function:
f(x)=-x^3+15x^2-48x+45
1st derivative -3x^2 + 30x - 48 = 0
2nd derivative -6x + 30 = 0 --> x = 5
f(5) = 55
--> Point of inflection at (5,55)
It appears to be a point of symmetry, but I don't know how to confirm that.
-----------------
B. The function has a local minimum at (2,1). At what point does a local maximum occur?
1st derivative -3x^2 + 30x - 48 = 0
--> x = 2 (local minimum)
--> x = 8 (local maximum)
f(8) = 109
local max @ (8,109)
RELATED QUESTIONS
How are the vertex and the axis of symmetry of a quadratic function... (answered by Edwin McCravy)
The graph of a cubic function has a local minimum at (5,-3) and a point of symmetry at... (answered by greenestamps)
The point (5,4) lies on the graph of a quadratic function whose zxis of symmetry is x=2.... (answered by robertb)
The graph of a quadratic function passes through the origin and has
vertex (4, 16).... (answered by MathLover1,ikleyn)
Hi there tutors, I have a question that I don't know how to do. This is the equation :... (answered by KMST)
find the vertex and axis of symmetry and graph the function... (answered by josmiceli)
List the vertex , slope, axis of symmetry, and graph the function. 18.y = -(x-4)+4
a)... (answered by ikleyn)
3. Given the function f(x)=-x²-6x-2
(A)Determine the vertex;
(B)List the axis of... (answered by Gogonati)
For each quadratic function, (a) find the vertex and the axis of symmetry and (b) graph... (answered by josgarithmetic)