Let f : R → R be given by f(x)= array ll x^ 5 +5 x^ 4 +10 x^ 3 +10 x^ 2 +3 x+1, & x Then…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : R → R be given by
\[f(x)=\left\{\begin{array}{ll} x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+3 x+1, & x<0 ; \\ x^{2}-x+1, & 0 \leq x<1 ; \\ (2 / 3) x^{3}-4 x^{2}+7 x-(8 / 3), & 1 \leq x<3 ; \\ (x-2) \log _{e}(x-2)-x+(10 / 3), & x \geq 3 . \end{array}\right.\]
Then which of the following options is/are correct?
\[f(x)=\left\{\begin{array}{ll} x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+3 x+1, & x<0 ; \\ x^{2}-x+1, & 0 \leq x<1 ; \\ (2 / 3) x^{3}-4 x^{2}+7 x-(8 / 3), & 1 \leq x<3 ; \\ (x-2) \log _{e}(x-2)-x+(10 / 3), & x \geq 3 . \end{array}\right.\]
Then which of the following options is/are correct?
- f′ is NOT differentiable at x = 1
- f is increasing on (–∞, 0)
- f is onto
- f′ has a local maximum at x = 1
Answer
(A) f ′ is NOT differentiable at x = 1
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Limit _ x 0 (4^ x -1 )^ 3 ( x p ) (1+ x^ 2 3 ) =
- Let S be the set of all twice differentiable functions f from to such that for all x ∈(–1,1). For f ∈ S , let…
- For a ∈ R (the set of all real numbers), a ≠ –1, _ n (1^ a +2^ a + +n^ a ) (n+1)^ a-1 [(n a+1)+(n a+2)+ +(n…
- If y = ( ax + b cx + d ), then 2 dy dx ~d ^ 3 y dx ^ 3 is equal to
- If _ x 0 ( a^ x +b^ x +c^ x 3 )^ / x , (a, b, c, λ > 0) is equal to
- Given that for each a ∈ (0, 1), _ h 0^ + _ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this limit be g ( a ). In…
- Let denote the set of all real numbers. Let f : → be defined by f(x)= array cl 6 x+ x 2 x+ x & ext if x eq 0…
- The function f(x)= (1+a x)- (1-b x) x is not defined at x = 0. The value which should be assigned to f at x =…
More Limit, Continuity and Differentiability questions · Browse all practice questions