Concavity
Determine whether f(x) = x^2 is concave up or down.
Concave up
Find the zero of f(x) = x - 5.
x = 5
Determine the end behavior of f(x) = x^2.
As x -> -inf, f(x) -> inf
What is sin(0 degrees)?
0
Solve log(100).
2
Determine whether f(x) = -x^2 +4 is concave up or down.
Concave down
Find the zeros of f(x) = x^2 - 9.
x = 3
x = -3
Determine the end behavior of f(x) = -x^2.
As x -> inf, f(x) -> -inf
As x -> -inf, f(x) -> -inf
What is cos(90 degrees)?
0
Solve log_2(8).
3
Determine the concavity of f(x) = x^3 on the interval (0, inf).
Concave up
Find the zeros of f(x) = x^2 - 5x + 6.
x = 3
x = 2
Determine the end behavior of f(x) = x^3 - 2x.
As x -> inf, f(x) -> inf
As x -> -inf, f(x) -> -inf
Find coordinates on the unit circle at 45 degrees.
(sqrt(2)/2, sqrt(2)/2)
Solve for x: log(x) = 4
x = 10000
Find the point of inflection of f(x) = x^3 - 3x.
(0,0)
f(x) = x^3 - 4x^2 - 5x
x = -1
x = 0
x = 5
Determine the end behavior of f(x) = -2x^5 + 3x^2 - 1.
As x -> inf, f(x) -> -inf
As x -> -inf, f(x) -> inf
What is tan(135 degrees)?
-1
Expand: log(x^3 * y)
3log(x) + log(y)
Find all the intervals of concavity and points of inflection for f(x) = x^4 - 4x^3.
- Concave up on (-inf, 0) and (2, inf)
- Concave down on (0,2)
- Points of inflection: (0,0) and (2,-16)
x = -2
x = 1/2
x = 3
A polynomial has a degree of 6 and a negative leading coefficient. Determine its end behavior.
As x -> inf, f(x) -> -inf
As x -> -inf, f(x) -> -inf
Find the exact value of sin(330 degrees).
-1/2
Solve for x: log_3(x) + log_3(x - 6) = 2
x = 3 + 3 * sqrt(2)