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# For f x x name the type of function and describe each of the three transformations from the

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er-example (if false). (a) If |f | is integrable on [a, b], then f is also integrable on [a, b]. (b) If f = F ′ for some function F on [a, b], then f is continuous on [a, b]. (c) If g is continuous on [a,b], then g = G′ for some G on [a,b]. (d) If G(x) = ???? x g is differentiable at p ∈ (a, b), then g is continuous at p.
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Determine f (8) and justify the value.
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properties: f is differentiable everywhere f(x+y)=f(x)f(y) f(0) doesn't equal 0 f'(0) = 1 Show that f(0)=1 Show that f(x) > 0 Use the limit definition of a derivative to show that f'(x) = f(x) for all values of x
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1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.
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ave a horizontal tangent line at x = 1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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