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WorksheetsDefinition of a Derivative
Total questions: 15
Worksheet time: 2hrs 12mins
15x2
(5/4)x4
indeterminate
∞
f'(x)=
h→0lim(hf(x+h)−f(x))
x→clim(x−cf(x)−f(c))
dxdy
an equation for the slope of the tangent line
h→0lim(h5(x+h)2−5x2)
5x2
10x
10
DNE
It's the average rate of change of y=3x^2+4x-2 on the interval [-2, 1].
0
1
2
3
Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2+9 (be ready to show work on the test).
x^2
2x+9
2
2x
This is NOT a correct notation for a derivative
y ' (say it as "y prime")
f '(x) (say it as "f prime of x")
dy/dx
dx/dy
Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2-2x+3 (be ready to show work on the test).
y ' = 2x - 2
y ' = 2x^2
y ' = 2x
y ' = x^2
Write the slope of the line tangent to the graph of y=x^2-2 at the point x = 8.
2
-4
-8
-16
This is a line that touches the function at a given point and has a slope that is equal to the instantaneous rate of change at a given point.
normal line
tangent line
delta line
secant line
This is the equation of the line tangent to the graph of y=x^2+3 at the point x = -1.
y = -2x + 2
y = 2x + 2
-(1/2)x + (7/2)
y = (1/2)x + (7/2)
