Derivatives (Aiyana)
The opposite of a derivative...
What is an integral?
Another name for integral.
a) derivative
b) limit
c) antiderivative
d) chain rule
What is c) antiderivative?
The domain of f(x)= 1/x+4
a) (-∞,∞)
b) (-∞,0)U(0,∞)
c) (-∞,4)U(4,∞)
d) (-∞,-4)U(-4,∞)
What is (-∞,-4)U(-4,∞)?
To find the derivative of y=(-5x^2+1)4, you would use this rule.
What is the Chain Rule?
The idea that a continuous function on a closed interval has both a maximum and a minimum is the main property found in the…
a) Mean Value Theorem
b) Relative Extrema Theorem
c) Extreme Value Theorem
d) Rolle's Theorem
What is c) Extreme Value Theorem?
The derivative of the equation f(x) = -5x2
What is f'(x) = -10x?
The integral of y=6x2
What is y=2x3+C?
The end behavior of the function of -x45
a) As x approaches -∞, f(x) approaches -∞. As x approaches ∞ f(x) approaches ∞
b) As x approaches -∞ f(x) approaches ∞. As x approaches ∞ f(x) approaches -∞
c) As x approaches -∞ f(x) approaches ∞. As x approaches ∞ f(x) approaches ∞
d) As x approaches -∞ f(x) approaches -∞. As x approaches ∞ f(x) approaches -∞
What is b) As x approaches -∞ f(x) approaches ∞. As x approaches ∞ f(x) approaches -∞?
The rule that shows that the derivative of h(x)=5x6 is h'(x)=30x5
What is the Power Rule?
The Mean Value Theorem is used to find...
a) The slope of the function's tangent line
b) The slope of the function's secant line
c) The continuity of a function
d) The Mean Value Theorem can’t be applied to a function to find anything
What is a) The slope of the function's tangent line?
The derivative of the equation f(x) = cos(x)
What is f'(x) = -sinx?
The antiderivative of f(x)=12x5+3x2-5x
What is f(x)=2x6+x3-(5x2/2)+C?
This would be considered an even function...
a) f(x)=2x2+x+5
b) f(x)=15x6+x2
c) f(x)=x3+8x2+10
d) f(x)=3x4+4x3+5x2
What is b) f(x)=15x6+x2?
The derivative of a constant is...
a) 1
b) the constant
c) 0
d) the negative of the constant
What is a) 0?
(The Constant Rule)
DOUBLE JEOPARDY
The instrument that each person in this group played while in the band.
What is trumpet, baritone, percussion, flute, and French horn.
The derivative of the equation f(x) = (3x2 + 4)3
What is f'(x) = 18x(3x2 + 4)2 ?
The integral of f(t)=(t3+2)2
What is f(t)=(t7/7)+t4+4t+4+C?
The condition for an odd function...
a) f(-x)=-f(x)
b) f(x)=-f(x)
c) f(-x)=f(x)
d) f(x)=g(x)
What is d) f(-x)=-f(x)?
To find the derivative of y=(-5x^2+1)^4, you would use this rule.
What is the Quotient Rule?
According to the Fundamental Theorem of Calculus, to find the integral of (x^3+4) on the interval of [1,4], you would use this set-up.
a) [(4)3+4] + C
b) [(4)3 + 4] - [(1)3 + 4]
c) [(4)3 + 4] - [(1)3 + 4] + C
d) You can not use the Fundamental Theorem of Calculus to find this integral
What is b) [(4)3 + 4] - [(1)3 + 4]?
Under the First Derivative Test theorem, if f’(x) changes from negative to positive at c, then f has a ______ _______ at (c,f(c))
What is a relative manimum?
Find the particular solution given the integral
f(x) = 7x3-1 and f(2)=44
What is (7x4/4)-x+18?
The function f(x)=cosx...
a) odd
b) even
c) neither
What is b) even?
The derivative of g(x)=2x5tan(x)
What is g'(x)=2x5sec2x-10x4tanx
or g'(x)=2x4(xsec2x-5tanx)?
The slope of the line found by Rolle’s Theorem...
a) 2
b) 1
c) -1
d) 0
What is d) 0?