A function f (x) is defined as f (x) = {\\begin{array}{c}e^{x\end{array}, , x < 1 ; \ln ⁡x + ax^{2} + bx, , x \geq 1 ; }., where x ϵ R. Which one of the following statements is TRUE?

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

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 such that a + b = e

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

GATE Electrical Engineering (EE) 2017 Shift 1 Solved Paper

Question : 36 of 65

Marks: +1, -0

A function f (x) is defined as

f (x) = {\{\table e^{x}, , x < 1 ; \ln ⁡x + ax^{2} + bx, , x ≥ 1 ; }.

, where x ϵ R. Which one of the following statements is TRUE?

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