Which of the following statements is true for the function f(x)={x,x≥1x3,0≤x≤1x33−4x,x<0

Function is increasing in (−∞,−2)∪(0,∞) and decreasing in (–2,0).x=–2 is local maxima and x=0 is local minima. it is derivable ∀x∈R−{0,1} and continuous ∀x∈RHence it changes sign twice, once at x=-2 and another at x=0. .

Which of the following statements is true for the function f(x)={x,x≥1x3,0≤x≤1x33−4x,x<0

Function is increasing in (−∞,−2)∪(0,∞) and decreasing in (–2,0).x=–2 is local maxima and x=0 is local minima. it is derivable ∀x∈R−{0,1} and continuous ∀x∈RHence it changes sign twice, once at x=-2 and another at x=0. .

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Which of the following statements is true for the function $f (x) =$ ${\begin{array}{cc} \sqrt{x}, & x \geq 1 \\ x^{3}, & 0 \leq x \leq 1 \\ \frac{x^{3}}{3} - 4 x, & x < 0 \end{array}$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$f' (x)$ fails to exist for three distinct real values of $x$ .

$f' (x)$ changes its sign twice as x varies from $- \infty to \infty$

The function attains its extreme values at $x_{1}$ and $x_{2}$ , such that $x_{1} x_{2} > 0$

It is monotonic increasing $\forall x \in R$ .

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Function is increasing in $(- \infty, - 2) \cup (0, \infty)$ and decreasing in (–2,0).

$x = - 2$ is local maxima and $x = 0$ is local minima. it is derivable $\forall x \in R - {0, 1}$ and continuous $\forall x \in R$ Hence it changes sign twice, once at x=-2 and another at x=0. .