Home
Class 12
MATHS
Lert f:[a , b]vec be a function such tha...

Lert `f:[a , b]vec` be a function such that for `c in (a , b),f^(prime)(c)=f^(c)=f^(c)=f^(i v)(c)=f^v(c)=0.` Then `f` has a local extermum at `x=cdot` `f` has neither local maximum nor minimum at `x=c` `f` is necessarily a constant function it is difficult to say whether `a)or(b)dot`

A

f has local extremum at x = c

B

f has neither local maximum nor local minimum at x = c

C

f is necessarily a constant function

D

It is difficult to say whether (A) or (B)

Text Solution

Verified by Experts

The correct Answer is:
D
`f.(C) = f..(C) = f...(C) = f^(iv)(C) = f^(v) (C) = 0 `
Now if n is the least positive integer such that `f^n (C) ne 0` , then it is not clear whether n is even or odd. So nothing can be said whether `f(x)` has local extrema at x= c or not .
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 5

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 4

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 6

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

Lert f:[a , b]vec be a function such that for c in (a , b),f^(prime)(c)=f^(ii) (c)=f^(iii) (c)=f^(iv) (c)=f^v(c)=0. Then f (a)has a local extermum at x=cdot f (b)has neither local maximum nor minimum at x=c f (c)is necessarily a constant function (d)it is difficult to say whether a)or(b)dot

If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then (a) x=a is a maximum for f(x) (b) x=a is a minimum for f(x) (c)can not conclude anything about its maxima and minima (d) f(x) is necessarily a constant function.

A function f such that f'(a)=f''(a)=….=f^(2n)(a)=0 , and f has a local maximum value b at x=a ,if f (x) is

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .

Let f(x) be a polynomial of degree 3 such that f(-2)=5, f(2)=-3, f'(x) has a critical point at x = -2 and f''(x) has a critical point at x = 2. Then f(x) has a local maxima at x = a and local minimum at x = b. Then find b-a.

If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a ,f(x) has a (a) minimum value (b) maximum value (c)not an extreme point (d) extreme point

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; and 6x+5x^2,x >0 Then at x=0,f(x) (a) has a local maximum (b) has a local minimum (c) is discontinuous (d) none of these

The function f: C -> C defined by f(x) = (ax+b)/(cx+d) for x in C where bd != 0 reduces to a constant function if

If f(x)=|[0,x-a, x-b], [x+a,0,x-c], [x+b, x+c,0]|,t h e n (a) f(a)=0 (b) f(b)=0 (c) f(0)=0 (d) f(1)=0