Slope of a line
Find the slope of the line: y = 2x
2
What is the derivative of x2?
2x
If y = x2 + 3x - 2, find dy/dx when x = 1
4
What is a tangent line in relation to a curve?
Find the slope of y = 4x +7
4
What is the derivative of 3x2 ?
6x
If f(x) = 2x3 - x2 + 4 then find f'(x) when x = 3
48
What does it mean if the derivative of a function is positive?
The function is increasing at that point.
y = 3x + 4 is a linear function. Find dy/dx.
3
2x - 2
f(x) = 1/3x3 + 2x2 - 5x + 4. Find f'(x) when x = 2
7
What does it mean if the derivative of a function is negative?
The function is decreasing at that point.
f(x) = 1.5x - 2. Find f'(x).
1.5
Find the derivative of y = 1 - 2x + 3x2
-2 + 6x
If A = 3k2 + 2k, find dA/dk when k = 4
26
What does the derivative represent?
The rate of change of one variable with respect to the other
OR: The slope of the curve at a point
y = 2x + 4
If f(x) = 1/2x2 + 4x - 5
x + 4
-25
Why is the derivative of a constant function always zero? Example, f(x) = 3
The graph of a constant function like f(x) = 3 is a horizontal line, so the slope would be 0.
Also, the derivative measures the rate of change of a function, so for a constant function, the function remains unchanged as x changes, so the rate of change is 0.