find the absolute extremum, if any, given by the second derivative test for each function

2. Consider the function f (x) = x¹ − 2x² + 3. (a) Find the intervals on which f is increasing / decreasing. (b) Find the intervals on which f is concave up/ concave down. Display your answer in table form, with a column for the intervals, columns for each factor, a column for the derivative, and a column for the function, as shown in lecture.

Determine if the following function (image 1) is derivate at the indicated value. If so, indicate the value of the respective derivative. Justify if not is derivate. Value: x=1

please show the COMPLETE SOLUTION

Choose the correct answer.   By definition, we call a function differentiable at a closed interval [a, b] if it has:       [a right-hand derivative, a derivative, a left-hand derivative]  at every point in the open interval (a, b),       [a right-hand derivative, a derivative, a left-hand derivative]  at the endpoint a, and       [a right-hand derivative, a derivative, a left-hand derivative]  at the endpoint b.

i.) Piecewise functions: a. have limits for their entire domain  b. have a domain of xER c. none of the other answers are correct d. never have limits for their entire domain   ii.) The instantaneous rate of change for the function of f(x) equals the derivative of f(x): a. True b. False

9) Find the second derivative of the function given below and evaluate it for x=1