A function f (x) is defined as \(g\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {{e^x},}&{x < 1}\\ {\ln x + a{x^2}+bx,}&{x \ge 1} \end{array}} \right.\), where x ϵ R. Which one of the following statements is TRUE?

f(x) is differentiable at x = 1 for all values of a and b such that a + b = e

f(x) is NOT differentiable at x = 1 for any values of a and b

f(x) is differentiable at x = 1 for the unique value of a and b.

f(x) is differentiable at x = 1 for all values of a and b.

A function f (x) is defined as \(g\left( t \right) = \left\{ {\begin{a

1.	A function f (x) is defined as \(g\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {{e^x},}&{x < 1}\\ {\ln x + a{x^2}+bx,}&{x \ge 1} \end{array}} \right.\), where x ϵ R. Which one of the following statements is TRUE?
A.	f(x) is NOT differentiable at x = 1 for any values of a and b
B.	f(x) is differentiable at x = 1 for the unique value of a and b.
C.	f(x) is differentiable at x = 1 for all values of a and b such that a + b = e
D.	f(x) is differentiable at x = 1 for all values of a and b.
Answer» C. f(x) is differentiable at x = 1 for all values of a and b such that a + b = e

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A function f (x) is defined as \(g\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {{e^x},}&{x < 1}\\ {\ln x + a{x^2}+bx,}&{x \ge 1} \end{array}} \right.\), where x ϵ R. Which one of the following statements is TRUE?

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