1) The graph of the derivative f ' of a continuous function f is shown. (Assume...

1) The graph of the derivative f ' of a continuous function f is shown. (Assume the function f is defined only for 0 < x < ∞.)

(a) On what interval(s) is f increasing? (2a) On what interval(s) is f decreasing?

(b) At what value(s) of x does f have a local maximum? (2b) At what value(s) of x does f have a local minimum? x=?

(c) On what interval(s) is f concave upward? (2c) On what interval(s) is f concave downward?

(d) State the x-coordinate(s) of the point(s) of inflection. x=?

2) Consider the following function.

f(x) = 1 + 5/x - 2/x^2

(a) Find the vertical asymptote(s). X=? (2a) Find the horizontal asymptote(s). Y=?

(b) Find the interval where the function is increasing. (2b) Find the interval where the function is decreasing.

(c) Find the local maximum and minimum values. "Local max & min"

(d) Find the interval where the function is concave up. (2d) Find the interval where the function is concave down.

Find the inflection point. (x,y)

3) Find the local maximum and minimum values of f using both the First and Second Derivative Tests.

f(x) =( x^2)/(x-2) "local max & min"

Expert Solution

milcah answered 1 year ago

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1) The graph of the derivative f ' of a continuous function f is shown. (Assume...

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