Derivatives Flashcards
dy/dx is called the _________________
Derivative (of a function “y =”)
f ‘ (x) is called the __________________
Derivative (of a function “f(x) = “)
When we substitute a number for x in dy/dx, we get the ______________
Slope of the tangent line at that value of x
f ‘ (a) gives us
Slope of the tangent line at x = a
f(a) gives us
A coordinate point (x,y) at x = a
Substitute a number for x in a “y =” equation to get
A coordinate point (x,y)
A __________ line touches a graph at exactly one point (with some exceptions)
Tangent
Another word for gradient
Another word for slope
If a function uses D and t instead of y and x, then the derivative is
dD/dt
Another word for slope and gradient is the _________ of ___________
Rate of change
If a graph shows distance (y) vs. time (x) then the derivative gives us
distance over time, or speed
To find the derivative of a term, we…
Bring down the exponent number and multiply it by whatever is next to the x, then subtract the exponent by 1.
If f(x) = x² + 7, then f’(x) = _____
f’(x) = 2x
If f ‘ (x) = 3x², then f(x) = _____
f(x) = x³ + c (we don’t know what c is without more information)
The slope of the tangent line at any local maximum or minimum value is ____
Slope at any local maximum or minimum is zero.
The value of the derivative at any local maximum or minimum is ____
Value of derivative at any maximum or minimum is zero.
At any local max or min, f’(x) = ___
f’ (x) = 0
At any local max or min, dy/dx = ____
dy/dx = 0
The derivative of ax is just ___
a
The derivative of any number without an x is ____
zero (e.g., derivative of 5 is 0)
1/x² can be rewritten as
x^(−2) (x to the power of negative two)
7/x³ can be rewritten as
7x^(−3) (seven times x to the power of negative three)
