Derivatives
D/dx Sin = ?
Cosx
Integral of sinxdx = ?
-cosx + C
What is the ONE condition needed to fulfill the Extreme Value Theorem?
Continuous
What happens to f when f' is greater than 0?
f is increasing.
If the velocity of a particle is positive, in what directions could the particle be moving? (Hint: It is literally an incredibly simple question)
Up or to the right.
D/dx ex = ?
ex
Integral of secxtanxdx = ?
secx + C
What TWO Conditions must be met for the Mean Value Theorem?
Continuous
Differentiable
What does a function have when f'(x) = 0 and changes from DECREASING to INCREASING?
A relative minimum
x(b)-x(a)/b-a
D/dx tanx = ?
sec^2x
Integral of a^x dx = ?
(a^x/lna) + C
What is a brief definition of the Rolle's theorem
If f(a) and f(b) are the same, the slope of f(c) must equal 0.
For the equation -2x^3 + 6x + 5, find the critical numbers that are less than 0.
-1
How do displacement and distance differ?
Distance is calculated with an absolute value while displacement is not.
D/dx csc = ?
-cscxcotx
Integral of ex dx= ?
e^x + C
What is the formula for the Mean Value Theorem
f'(c) = f(b) - f(a) / b - a
If a function's slope is positive, will a right reimann sum be an over or underestimate?
Overestimate.
It switches from going right to left or from going up to down.
If f and g are inverses, then g'(x) = ?
1/f'(g(x))
Integral of 1/(x^2)+1 dx = ?
tan^(-1)x + C
Which theorems MUST be CONTINUOUS
Rolles, MVT, EVT, IVT
If f'(x) is decreasing, what is the quality of the function's concavity?
It is negative.
If acceleration and velocity are both negative, is a particle speeding up or slowing down?
Speeding up.