Reference no: EM131017559
Using Graphing Utilities to Estimate Slope:
Let f(x) = {|x|, x does not equal 0
And f(x) = {1, X = 0
(Sorry but I cannot figure out how to make a huge bracket that houses both quantities. I'm new to calculus)
a) Use a graphing utility to graph f in the viewing window -3 ≤ x ≤ 3, -2 ≤ y ≤2. What is the domain of f? Show your work.
b) Use the zoom and trace features of a graphing utility to estimate: The limit as x →0 f(x). Please show your work.
c) Write a short paragraph explaining why the function f is continuous for all real numbers.
d) Visually estimate the slope off at the point (0, 1).
e) Explain why the derivative of a function can be approximated by the formula below for small values of Δx.
(f (x + Δx) - (f (x - Δx)) / 2 Δx
Use the next formula to approximate the slope of fat the point (0, 1).
f' (0) = (f (0 + Δx) - (f (0 - Δx)) / 2 Δx = (f(Δx) - (Δx)) / 2 Δx
What do you think the slope of the graph off is at (0, 1) ?
(keep scrolling)
f) Find a formula for the derivative off and determine f'(0). Write a short paragraph explaining how a graphing utility might lead you to approximate the slope of a graph incorrectly.
g) Use your formula for the derivative off to find the relative extrema off Veryify your answer using a graphing utility. Show your work.
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