There are three things you have to know:
- A function is convex when its second derivative
- A function is concave when it second derivative
- The derivative of a power,
, is 
So, the first derivative is
and the second derivative is
This implies that the second derivative of a parabola is constant, and of course that 2 doesn't change the sign of 
.
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
Answer:
e
Step-by-step explanation:
where is the picture and please explain problem
Answer:
6:15:11
Step-by-step explanation:
We first start off with 24:60:44. We then know that the greatest common factor is 4, so we divide the ratio by 4 to get 6:15:11.
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