Let f:\mathbb{R}\to\mathbb{R} be given by f(x)=\{\table x^5+5x^4+10x^3+10x^2++3x+1\text{,},x < 0\text{;};x^2-x+1\text{,},0 \leq x < 1\text{;};2/3x^3-4x^2+7x-8/3\text{,},1 \leq x < 3\text{;};(x-2)\log_e(x-2)-x+10/3\text{,},x \geq 3.Then which of the following options is/are correct? [JEE Adv 2019 P1]

f' is NOT differentiable at x=1

Limits, Continuity and Differentiability

Section: Mathematics

Question : 21 of 51

Marks: +1, -0

Let f:ℝ→ℝ be given by

f(x)={

x5+5x4+10x3+10x2++3x+1,

x<0;

x2−x+1,

0≤x<1;

x3−4x2+7x−

1≤x<3;

(x−2)loge(x−2)−x+

x≥3.

Then which of the following options is/are correct?

[JEE Adv 2019 P1]

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