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WorksheetsGraphs of f, f', and f''
Total questions: 23
Worksheet time: 30mins
Which one of the following statements is always true?
When a graph is increasing, its derivative is negative.
When a graph is decreasing, so is its derivative.
When a graph is decreasing, its derivative is negative.
When a graph is increasing, so is its derivative.
f(x) is a polynomial function. Which one of the following statements is FALSE?
f(x) has a derivative of zero when the graph of f has a relative min or max.
If the derivative of f(x) changes from positive to negative at some point, then the graph of f has a relative minimum at that point.
If the derivative of f(x) is always positive, then the graph of f has no relative extrema.
If the graph of f is always increasing, then the derivative of f(x) is never negative.
g(x)=2x3-3x2
Select the correct derivative of f(x).
A.
B.
C.
D.
7.
(A)
(B)
(C)
(D)
If (a,b) is a local minimum, then what will be true about f''(a)?
It's postive
It's negative
It's zero
Cannot be determined
For what values of x does f(x) have a horizontal tangent?
-3.5, 3.5
-5, 5
there are no horizontal tangents
-5, 0, 5
According to the graph, at the point x=-2, is f(x) increasing or decreasing and why?
At x=-2 f(x) is increasing because the graph has a positive slope.
At x=-2 f(x) is decreasing because the graph has a positive slope.
At x=-2 f(x) is decreasing because the graph lies below the x-axis.
At x=-2 f(x) is decreasing because the graph has a negative slope
Which graph represents the derivative of this graph?
The graph of f is shown above.
Which graph represents the graph of f'(x)?
Is the above function differentiable for all values of x? Why?
Yes, the slope of the tangent line can be calculated for all values of x.
Yes, the function is continuous for all values of x so the function is differentiable.
No, the function has a sharp turn in the first quadrant so if is not differentiable.
No, the function is discontinuous so it is not differentiable.
