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S25_CTMS-25_Elements of Calculus
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Let . What is the value of over the interval such that the Mean Value Theorem is satisfied?
Which of the following is not a requirement for the Mean Value Theorem to hold?
Given and knowing that the equation has 3 distinct real solutions which of the following is always true?
Which of the following functions is guaranteed to have a critical point with by Rolle’s Theorem?
The Softplus function is defined as What is the derivative of Softplus and where is it defined?
Consider the equation . Find by implicit differentiation.
Find the derivative of .
Choose the expression equivalent to . Hint: Recall that and use differentiation.
Calculate , i.e., the third derivative of the function.
Calculate where is a constant.