Consider a function f(x) that has all of the properties listed below. For each o

Question

Consider a function f(x) that has all of the properties listed below. For each of the properties, write (in words) what the property means for tin* graph of f(x). For example, for part (a) about continuity, one could write: Since f is continuous on the entire interval [-3.5], this means f(x) can be drawn from x = -3 to x = 5 without any breaks or vertical asymptotes in the graph. Sketch the graph of a function f that has all of the properties. The domain of f is the interval [-3,5], and f is continuous on the entire interval [-3,5]. f^'(x) > 0 on the interval (1,3), mid f^'(x)

Explanation / Answer

(a) The domain of f(x) in interval [-3,5] means function is not defined on this interval. f(x) is continuous on this interval means f( x) can be drawn from x=-5 to x=5 without any break.

(b)

f(x)>0 means that when x is negative, the slope f(x) (well, actually the slope of the line tangent to f(x)) is positive

f(x)<0 means that when x is positive, the slope f(x) (well, actually the slope of the line tangent to f(x)) is negative.

(c) f''(x)<0 there is an inflection point changing the concavity of f(x)

(d) f'(x)=0 means that function f(x) is almost constant around the value x.

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