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]
False
false
point is 1 dimentional
lines are infinite
fals for both
Answer:
the last one
Step-by-step explanation:
In the last one, it takes all of the numbers in the one parentheses and distributes it to the 0.5.
Look at the picture. (sorry for the messy writing)
Answer:
annual
Step-by-step explanation:
You make a single deposit of $100 today. It will remain invested for 4 years at 8% per year compounded annually. What will be the future value of your single deposit at the end of 4 years?
Y results from something being multiplied by x , and the values are always proportional to one another. Notice that putting these points into a ratio of x-value to y-value results in 1:3 as a simplified version. So, the constant of proportionality is what x is being multiplied by to get y . In this case, it is 3 . PLEASE MARK A THE BRAIN THINGY
