Find maximum and minimum value of y=x^3+6x^2-15x+7 calculator
Result:
Type: No maximum (parabola opens upward)
How It Works
1
Enter Function
Input coefficients
2
Set Domain
Choose interval
max
Find maximum
Common Examples
f(x) = -x² + 4x - 3
Maximum at x = 2, y = 1
f(x) = -2x² - 8x - 6
Maximum at x = -2, y = 2
Vertex: x = -b/(2a)
For quadratic functions ax² + bx + c (a < 0)
Absolute Maximum Calculator
📈
What
Find the highest point (global maximum) of a mathematical function.
🎯
Why
Essential for optimization problems, calculus, and finding optimal solutions.
⚡
Applications
Engineering optimization, economics, physics, and mathematical analysis.
📊 Calculation Examples
f(x) = -x² + 4x - 3
Max x:2
Max y:1
Global Maximum
f(x) = -2x² - 8x - 6
Max x:-2
Max y:2
Global Maximum
f(x) = -x² - 1
Max x:0
Max y:-1
Global Maximum
Frequently Asked Questions
1
What is an absolute maximum?
The absolute maximum is the highest value a function attains over its entire domain.
2
How do I find the maximum of a quadratic?
For f(x) = ax² + bx + c with a < 0, the maximum occurs at x = -b/(2a).
3
What if the parabola opens upward?
If a ❭ 0, the parabola opens upward and has no maximum (only a minimum).
4
How do intervals affect the maximum?
On a closed interval, check the vertex and endpoints to find the absolute maximum.
5
What about linear functions?
Linear functions have no maximum on all reals, but may have one at interval endpoints.
Maximum Formulas
x = -b/(2a)
Quadratic vertex
Check endpoints
For intervals
Quick Examples
-x² + 4x - 3
Max at (2, 1)
-2x² - 8x - 6
Max at (-2, 2)
💡 Tips
• a < 0: parabola opens down (has max)
• a > 0: parabola opens up (no max)
• Check vertex and endpoints
• Linear functions: check endpoints