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:
<--------
<----|---|---|---|---|---|---|----------
-9 -8 -7 -6 -5 -4 -3
Step-by-step explanation:
Answer:
The mean score is 87
Step-by-step explanation:
79x2=158
158-71=87
Perpendicular equation: y=-1/5x + 6
25.2:360 ::x:5100
Or 25.2 x ------=----- then cross multiply, 360x=5100*25.2
