Consider the function f defined by sin (52) +8, if x < 0 I (a -...

Transcribed Image Text:

Consider the function f defined by sin (52²) +8, if x < 0 I (a - b)x+ 2a, if x ≥ 0 f(x) = a) Determine the value of the constant a for which f is continuous at r = 0. You must carefully justify your answer. b) Determine the values of the constants a and b for which f is differentiable at x = 0. You must carefully justify your answer. Consider the function f defined by sin (52²) +8, if x < 0 I (a - b)x+ 2a, if x ≥ 0 f(x) = a) Determine the value of the constant a for which f is continuous at r = 0. You must carefully justify your answer. b) Determine the values of the constants a and b for which f is differentiable at x = 0. You must carefully justify your answer.