Differentiability Consider the following piecewise defined function f(x) { f(x) = { 2x^2 - 4x -...

 

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Differentiability Consider the following piecewise defined function f(x) { f(x) = { 2x^2 - 4x - 1, { - x^2 + 14x - 28, x>3 x <= 3 } 2x2 - 4x - 1, X<3 f(x) -x2 + 14x - 28, x<3 a) Use the rules for derivatives to find the rule for f'(x) the derivative of the piecewise function f(x) b) Use one-sided limits of f(x) to determine whether the derivative exists at x = 3. (Evaluate one sided limits lim f'(x) lim f'(x) x- 3+ X- 3- and make the conclusion regarding differentiability at x=3.) { lim_{x -> 3^+} f(x) lim_{x -> 3^-} f(x) } QUESTION 2 Apply the product rule to find the derivative of each of the following functions f(x) = (2x2 + 4x + 3) e* a) { f(x) = (2x^2 + 4x + 3) e^x } %3! b) g(x) = cos? x = (cos x) (cos x) { g(x) = cos^2 x = (cos x) (cos x) } Differentiability Consider the following piecewise defined function f(x) { f(x) = { 2x^2 - 4x - 1, { - x^2 + 14x - 28, x>3 x <= 3 } 2x2 - 4x - 1, X<3 f(x) -x2 + 14x - 28, x<3 a) Use the rules for derivatives to find the rule for f'(x) the derivative of the piecewise function f(x) b) Use one-sided limits of f(x) to determine whether the derivative exists at x = 3. (Evaluate one sided limits lim f'(x) lim f'(x) x- 3+ X- 3- and make the conclusion regarding differentiability at x=3.) { lim_{x -> 3^+} f(x) lim_{x -> 3^-} f(x) } QUESTION 2 Apply the product rule to find the derivative of each of the following functions f(x) = (2x2 + 4x + 3) e* a) { f(x) = (2x^2 + 4x + 3) e^x } %3! b) g(x) = cos? x = (cos x) (cos x) { g(x) = cos^2 x = (cos x) (cos x) }