Let f(x)=3x^2+6x-10For which input x is the value of the function a minimum?

In summary, for a quadratic function, the value of x = -b/2a will give the stationary point, which can be either a maximum or a minimum depending on the value of the coefficient a.
  • #1
Jurrasic
98
0
And what is the minimum value?
( -b/2a is for a maximum problem, but how do you get through this kind of problem?)
 
Physics news on Phys.org
  • #2
x=-b/2a will give you the stationary point for the quadratic. In f(x) =ax^2+bx+c, if a>0 is the stationary point maximum or minimum?
 
  • #3
Jurrasic said:
And what is the minimum value?
( -b/2a is for a maximum problem, but how do you get through this kind of problem?)
For the quadratic, ax2 + bx + c:

If the coefficient of x2, which is a, is negative, then x = -b/2a, gives the x coordinate of the maximum.

If the coefficient of x2, which is a, is positive, then x = -b/2a, gives the x coordinate of the minimum.
 

1. What is the minimum value of the function?

The minimum value of the function cannot be determined without knowing the input value, as the function can have different values for different inputs.

2. How do you find the minimum value of the function?

The minimum value of the function can be found by finding the input value that results in the lowest output value. This can be done by using the vertex form of the function, -b/2a, where a, b, and c are the coefficients of the quadratic equation.

3. Can the minimum value of the function be negative?

Yes, the minimum value of the function can be negative if the input value results in a negative output value. In this case, the minimum value would be the lowest negative value.

4. What is the vertex of the parabola?

The vertex of the parabola is the point where the function reaches its minimum or maximum value. In this case, the vertex can be found by using the formula -b/2a to find the x-coordinate and then plugging that value into the original function to find the y-coordinate.

5. Can the minimum value of the function be the same for different input values?

No, the minimum value of the function will be different for different input values. This is because the function is a parabola and the lowest point (minimum value) will shift depending on the input value.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
21
Views
2K
  • Precalculus Mathematics Homework Help
Replies
15
Views
497
  • Precalculus Mathematics Homework Help
Replies
12
Views
912
  • Precalculus Mathematics Homework Help
Replies
3
Views
825
  • Precalculus Mathematics Homework Help
Replies
10
Views
766
  • Precalculus Mathematics Homework Help
Replies
6
Views
549
  • Precalculus Mathematics Homework Help
Replies
7
Views
721
  • General Math
Replies
5
Views
732
  • Precalculus Mathematics Homework Help
Replies
11
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
540
Back
Top