Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have
f'(x) = 2ax + b
and
f''(x) = 2a
Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.
(i) f is concave up when f'' > 0, which occurs when a > 0.
(ii) f is concave down when f'' < 0, and this is the case if a < 0.
In Mathematica, define f by entering
f[x_] := a*x^2 + b*x + c
Then solve for intervals over which the second derivative is positive or negative, respectively, using
Reduce[f''[x] > 0, x]
Reduce[f''[x] < 0, x]
Answer:
Hemisphere Formulas in terms of radius r:
Volume of a hemisphere: V = (2/3)πr.
Step-by-step explanation:
Answer:
2nd option
y > 6 and y < 2
Step-by-step explanation:
as the value of y can not be greater than 6 and less than 2 at the same time, the 2 inequalities have no common solutions
theefore no solution
I think it measures an angle of 180 degrees
Answer:
7y + 24
Step-by-step explanation:
Think of the negative sign to the left of the parentheses as being -1. Then apply the distributive property. The effect of a negative sign to the left of parentheses or a 1 to the left of parentheses is that each term inside the parentheses changes sign.
-(-7y - 24) = -1(-7y - 24) = (-1)(-7y) - (-1)(24) = 7y - (-24) = 7y + 24
