Vocabulary
f (x) is concave up when…
What is: When f ′(x) is increasing OR f "(x) > 0
What is the derivative of: y = 6x5 – x + 10
What is: y' = 30x4 - 1
Evaluate: ∫ (x5 + 3x2 – x + 1)dx
What is:
(1/6)x6 + x3 - (1/2)x2 + x + C
Extreme Value Theorem: If f is continuous on a closed interval, then…
What is… f must have both an absolute maximum and an absolute minimum on the interval.
How do we remember the Quotient Rule?
What is:
"Lo d-Hi minus Hi d-Lo, all over the square of what's below!"
The "+ C" of an antiderivative represents...
What is: a constant
Calculate the derivative of the function:
f(x) = ex(x2 + 1).
What is:
f'(x) = ex(x2 + 1) + 2x(ex)
Evaluate: ∫ sin(x) dx
What is: -cos(x) + C
Fundamental Theorem of Calculus (Part 1): If f is an integrable function and g(x) = ∫ f(x)dx on the interval [a, b], then
What is:
∫ f(x)dx on the interval [a, b] = g(b) - g(a)
A particle changes direction when…
What is: velocity changes signs.
To find extreme values of a closed-interval function, look for where…
What is: f ′ is zero or undefined (critical points) AND f has endpoints.
Calculate the derivative of the function:
f(x)= ln(tan(x))
What is:
f'(x) = sec2x/tanx
Evaluate: ∫ 1/x3 dx
What is: -1/2x2 + C
Mean Value Theorem: If f(x) is differentiable on (a, b) and continuous on [a, b], then there is at least one number x = c in (a, b) such that...
What is:
f'(c) = [f(b) - f(a)] / [b - a]
If a graph is concave up on a right Riemann sum, is it an overestimate or an underestimate?
What is: an overestimate
Name FOUR ways in which a function can fail to be differentiable at a point.
What is: Discontinuity • Corner • Cusp • Vertical tangent line
If h(x) = f(g(x)) and f(2) = 5, f'(2) = 6, g(3) = 2 and g'(3) = 5, Find h'(3).
What is: 30
Evaluate: ∫ sec(x) tan(x) dx
What is: sec(x) + C
Fundamental Theorem of Calculus (part 2): If g(x) = ∫ f(t)dt on the interval [2, x2], then g'(x) =
What is:
g'(x) = f(x2)*2x
The limit definition of the derivative is...
What is:
lim h→0 [f(x + h) - f(x)] / h
Exponential Growth or Decay: If dy/dx = ky, then the general solution to the Differential Equation is...
What is: y = Cekt, where C is the quantity at t = 0, and k is the constant of proportionality.
Calculate dy/dx:
3x - x2y = e4
What is:
dy/dx = (3 - 2xy) / x2
Evaluate: ∫ cos(2x) dx
What is:
(1/2)sin(2x) + C
Intermediate Value Theorem: If f is continuous for all x in interval [a, b] and y is a number between f(a) and f(b), then...
What is:
There exists a number x = c, where a < c < b, for which f(c) = y.
Ms. Schreuder is really sad that...
What is: THIS IS SENIORS' LAST DAY