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Derivatives and Continuity

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A #calculus quiz about #derivatives and #continuity

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Questions 11

Answers

1
Which secant line best approximates the derivative of the function at x₀?
x0 to x0+ h2
x0 to x0+ h3
x0 to x0+ h1
2
In the slope of the tangent equation line why does h --> 0?
The h value is insignificant.
The h value ends up cancelling out.
It forces the secant line to look like the tangent line.
As h --> 0, the limit does not exist.
3
The red line shown is a
curved line
tangent line
asymptote
secant line
4
Calculating the slope of which line will produce the instantaneous rate of change at point P?
Tangent Line
Curved Line
Horizontal Asymptote
Secant Line
5
If a function is increasing, the derivative is
negative
positive
not enough information
zero
6
A derivative cannot be taken at a...
Corner
Cusp
All of the Above
Discontinuity
7
If a function is straight across (such as at a max or min), the derivative is
zero
negative
not enough information
positive
8
If a function is decreasing, the derivative is
positive
zero
negative
not enough information
9
You can find the derivative by...
Finding the slope of the secant line
taking the limit of the numerator and denominator
Finding the slope of the tangent line
Finding the average rate of change
10
In the slope of the tangent equation line what does h represent?
the instantaneous rate of change of the function
the height
The horizontal distance between x1 and x2
the vertical distance between y1 and y2
11
A Derivative is
the y-value that a function is approaching from both sides
the y-value that a function is approaching from one side
the instantaneous rate of change of a function
the slope of the secant line