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Differentiability
Derivatives
Curve Sketching
D, V, A
Antiderivatives & Tangent Lines
100
The function y = absolute value of x is NOT differentiable at this point because of a corner.
What is x = 0?
100
d/dx(sinx - cosx)
What is y = cosx + sinx?
100
If f'(x) is postive, then we know this about f(x).
What is f(x) is increasing?
100
This is the derivative of the position function.
What is the velocity function?
100
This is the antiderivative of f(x) = 3 times x cubed.
What is F(x) = (3/4) x to the fourth + C?
200
The function y = the cubed root of x is not differentiable at x = 0 because of this feature in the graph.
What is a "vertical tangent line"?
200
This function is the derivative of the square root of x, in simplified form.
What is 1/2 times the square root of x?
200
If f"(x) is positive, then we know this about f(x).
What is f(x) is concave up?
200
This is the second derivative of the position function.
What is the acceleration function?
200
This is the antiderivative of f(x) = the square root of x, in simplified form.
What is F(x) = (2/3) x to the 3/2 + C?
300
The function y = the cubed root of x squared is not differentiable at x = 0 because of this feature in the graph.
What is a "cusp"?
300
This is what the power rule says about y = x to the n power.
What is "the derivative is n times x to the n - 1?
300
If f'(x) is negative, then we know this about f(x).
What is f(x) is decreasing?
300
This is the velocity of a projectile with whose height is given by h(t) = -3 times t squared + 6 times t + 5 when t = 2
What is -6?
300
This is the antiderivative of f(x) = -3cosx.
What is F(x) = -3sinx + C?
400
The function y = 1/x is not differentiable at x = 0 for this reason.
What is the function is "discontinuous"?
400
d/dx(7 squared)
What is 0?
400
If f'(x) is increasing, then we know this about f(x).
What is f(x) is concave up?
400
This is the acceleration of a particle whose position function is given by s(t) = -2cost.
What is a(t)=2cost?
400
This is the equation of the tangent line to the curve y = the square root of x at x = 4.
What is y - 2 = (1/4)(x-4)?
500
The function y = abs(x)/x is differentiable on this set of values in interval notation.
What is (neg infinity, 0) U (0,infinity) ?
500
This is the definition of the derivative.
What is "the limit as h goes to 0 of (f(x+h)-f(x))/h?
500
This is where a curve changes concavity.
What is a point of inflection?
500
This is the acceleration of a particle whose velocity is given by v(t) = sin squared t + cos squared t.
What is 0?
500
This is the equation of the tangent line to y = 3sinx +2 at x = 0.
What is y - 2 = 3(x-0)?