Suppose the following data points are generated by a smooth function f(x): 1/3 2/3 4/3 5/3 2. f(x) 1.8415 1.9954 1.7231 1.1411 0.4987 0.0710 0.0411 The approximation of f(x) dx using the trapezoidal rule with 3 sub-intervals is:

Q: 8. Determine the intervals where the function is increasing or decreasing. Find the local maxima and…

A: First derivative test

Q: Sketch the graph of the f(x) below and state its domain and range. (Hint: V1/2 z 0.71) f(æ) = { 2x2…

A: For, x <_ 1/sqrt(2) the red part represents 2x2 - 1. For, x > 1/sqrt(2), the blue graph…

Q: Derivative Test. (d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c). (e)…

A: Solution is as follows:

Q: Find a value for the constant c so that the function с if x < 8 f(x) = { x-10 6x 1 - if x ≥ 8 is…

A:

Q: The locally linear approximation of the differentiable function f at x = 3 is used to approximate…

A: An approximation value is an overestimate if it is higher than the true value. A linear…

Q: Consider the four points given below, which satisfy the function f(x) = 1/x. f(x) 3.35 0.298507 3.40…

A: here is true value is find by function f(x)= 1/x so for f(3.44) = 1/3.44=0.2906977  and value obtain…

Q: Answer the following about the function f (x) = (1/3)x^3 − (1/2)x^2 −2x + 1 a. Find all critical…

A:

Q: 4 .. . 10) For the function f(x) = (x – 1) (x +3): a) Find the intervals of increase/decrease and…

A: