Written Explanations Flashcards
How do you explain a function is increasing?
The derivative is positive
How do you explain a function is decreasing?
The derivative is negative
How do you explain a function has a maximum?
The derivative changes from positive to negative
How do you explain a function has a minimum?
The derivative changes from negative to positive
How do you explain a point of inflection?
The second derivative changes signs
How do you explain Intermediate Value Theorem?
The function is continuous on the interval [a, b] and f(a) < y < f(b) so there is a value c in the interval (a, b) such that f(c) = y.
How do you explain Mean Value Theorem?
The function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) so there is a value k in the interval (a, b) such that fâ(k) = #
How do you explain a maximum at a left endpoint?
The derivative is negative to the right of the end point.
How do you explain a maximum at a right endpoint?
The derivative is positive to the left of the endpoint.
How do you explain a minimum at a left endpoint?
The derivative is positive to the right of the endpoint.
How do you explain a minimum at a right endpoint?
The derivative is negative to the left of the endpoint.
How do you explain a function is concave up?
The second derivative is positive.
How do you explain a function is concave down?
The second derivative is negative.
What should I write instead of the word it?
Write what it refers to. For example, the function, the derivative, the second derivative, etc.
