Derivatives
f(x)=3x
f'(x)=3
Estimate the limit as x approaches 3 of 3x
The limit as x approaches 3 is 9
The function f is given by 4x6-3x3+2. Describe the end behavior of f.
As input values decrease, the function increases and as input values increase, the function increases.
Is the function f(x) = 5x7-5x3 even or odd?
odd
What's the decimal form of 0.002%
0.00002
f(x)=19x2-3x
f'(x)=38x-3
How do you know if a limit exists based on a graph?
When the left-hand limit equals the right-hand limit, the limit exists.
The function h is given by h(x)=-3x5-4x3+2x2-10. Describe the end behavior of h as the input values increase without bound.
lim h(x) = -∞
x->∞
Two points are given: (0, 30), (12, 100)
If the line that crosses these points is constant, what is the rate of change?
5.83 (70/12)
What's the most simplified fraction form of 64%?
16/25
f(x)=5x3-7x2
f'(x)=15x2-14x
What is the average rate of change?
The average rate of change measures how much a function's output changes per unit, on average, over a specific interval.
Average Rate of Change=(f(b)−f(a))/(b−a)
For polynomial function g,
lim g(x) = ∞ and lim g(x) = -∞
x->-∞ x->∞
What is true about the function g of its degree and leading coefficient?
g is a odd function with a negative leading coefficient
Given the zero x = 2+3i, what are the other zeros of the polynomial function g(x) = x3-8x2+29x-52?
x=2-3i and x=4
What's 43% of 200?
86
f(x)=3x5+4x4
f'(x)=15x4+16x3
What is a complex conjugate?
A complex conjugate is a pair of complex numbers that share the same real part, but have imaginary parts with opposite signs.
How much wood could a woodchuck chuck, if a woodchuck could chuck wood?
Free Points
The leading term of the polynomial function p is axn, where a is a real number and n is a positive integer. The factors of p include (x-1), (x+i), and (x-(5+i)). What is the least possible value of n?
5
Find x:
x2+5=105
x=10
f(x)=(7x4+3)(8+x2)
f'(x)=42x5+224x3+6x
The limit of x as it approaches 4 is 0
A polynomial function f is given by
f(x) = axb where a is an integer and b is a positive integer. It is known that
lim f(x) = ∞ and lim f(x) = ∞
x->-∞ x->∞
What is true about the value of b in relation to the end behavior?
b is an even number
Classify the polynomial by degree and number of terms:
-3x3
cubic monomial
Find x:
6x+3=21
x=3