Unit 4-5 Test Review Practice Problems

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Mathematics
•
10th Grade - University
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the linear approximation of a function f(x) at a point x = a?
Back
The linear approximation of a function f(x) at a point x = a is given by the formula: y = f(a) + f'(a)(x - a).
2.
FLASHCARD QUESTION
Front
How do you find the acceleration from a position function x(t)?
Back
To find the acceleration from a position function x(t), take the second derivative of x(t) with respect to time t: a(t) = x''(t).
3.
FLASHCARD QUESTION
Front
What does it mean if f'(c) = 0 and f''(c) > 0 at a point c?
Back
If f'(c) = 0 and f''(c) > 0, then there is a local minimum at x = c.
4.
FLASHCARD QUESTION
Front
How can you determine if a particle is moving left based on its velocity function?
Back
A particle is moving left when its velocity function v(t) is negative, i.e., v(t) < 0.
5.
FLASHCARD QUESTION
Front
What is a relative minimum in the context of a function's graph?
Back
A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points.
6.
FLASHCARD QUESTION
Front
What is the significance of the first derivative f'(x)?
Back
The first derivative f'(x) represents the rate of change of the function f(x) and indicates the slope of the tangent line at any point x.
7.
FLASHCARD QUESTION
Front
What does the second derivative f''(x) tell us about a function?
Back
The second derivative f''(x) indicates the concavity of the function: if f''(x) > 0, the function is concave up; if f''(x) < 0, the function is concave down.
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