If f(x)={(sin(x^(2)-3x),xle0 6x+5x^(2)...

If `f(x)={(sin(x^(2)-3x),xle0`
`6x+5x^(2),xgt0` then at x=0, f(x) is?

A

f(x) has a local minima

B

f(x) has a local maxima

C

f(x) has point of inflection

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

1

f(x)=sin 0 =0
`f(x)^(+))rarr(0^(+))`
`f(0^(+))=underset(xrarr0)lim sin (x^(2)-3x)=underset(hrarr0)limsin (h^(2)+3h)rarr0^(+)`
Thus `f(x^(+)) and f(0^(-))gtf(x)`
Hence x =0 is point of manima

Promotional Banner

Promotional Banner

Topper's Solved these Questions

MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Multiple correct answers type|48 Videos
MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Linked comprehension type|50 Videos
MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Concept Application Exercise 6.7|5 Videos
METHODS OF DIFFERENTIATION
CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos
MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a function defined as f(x)= {(sin(x^2-3x),xle0),(6x+5x^2,xgt0):} Then at x=0,f(x)

If f(x) = (sin 5x)/(2x) (when x!=0 ) = (5k)/4 (when x= 0), and f(x) is continuous at x=0, find k.

If f(x)={((sin5x)/(x^(2)+2x),"when "x ne 0),(k+(1)/(2),"when "x =0):} is continuous at x=0, then the value of k is-

If f(x)={(x"sin"(1)/(x),"when "x ne 0),(0,"when "x =0):} then at x = 0, the function f(x) is -

Let f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):} Discuss the continuity of f (x) at x = 0 .

If f'(x)=(1-2sin^2x)/f(x), (f(x) ge 0, AA x in R and f(0)=1) then f(x) is a periodic function with the period

int(x^(2)-1)/(x^(4)+3x^(2)+1)dx(xgt0) is

Let f(x)=int_0^x(cost)/tdt(xgt0): then at x=(2n+1)pi/2nin1, f(x) has

If f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal to

If f(x)=x^2-3x+1 , then find f(0) .

CENGAGE PUBLICATION-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise

Let f(x)={(|x|,for 0<|x|lt=2), (1,"for"x=0):} Then at x=0, f(x) has ...
Text Solution
|
If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...
Text Solution
|
If f(x)={(sin(x^(2)-3x),xle0 6x+5x^(2),xgt0 then at x=0, f(x) is?
Text Solution
|
The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...
Text Solution
|
The function f(x)=(4sin^2x-1)^n(x^2-x+1),n in N , has a local minimum...
Text Solution
|
The true set of real values of x for which the function f(x)=xlnx-x+1 ...
Text Solution
|
All possible value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...
Text Solution
|
The function f(x)=(ln(pi+x))/(ln(e+x)) is
Text Solution
|
If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...
Text Solution
|
Let f(x)={x+2,-1lelt0 1,x=0 (x)/(2),0ltxle1
Text Solution
|
If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0
Text Solution
|
A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...
Text Solution
|
Let the function f(x) be defined as follows:f(x)= x^3 +x^2 −10x,−1≤x<...
Text Solution
|
Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x...
Text Solution
|
F(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)
Text Solution
|
Let h(x)=x^(m/n) for x in R , where m and n are odd numbers where 0<...
Text Solution
|
The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the i...
Text Solution
|
The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 ...
Text Solution
|
The maximum value of x^4ehat-x^2 is e^2 (b) e^(-2) (c) 12 e^(-2) (d...
Text Solution
|
If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (c^2)/(sqrt(a b...
Text Solution
|