If f has a local extremum at a and if f'...

If f has a local extremum at a and if f'(a) exists then

`f'(a) lt 0`

`f'(a) gt 0`

`f'(a) = 0`

`f''(a) = 0`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATIONS OF DIFFERENTIAL CALCULUS
PREMIERS PUBLISHERS|Exercise Problems For Practice (Answer the following question)|39 Videos
APPLICATIONS OF DIFFERENTIAL CALCULUS
PREMIERS PUBLISHERS|Exercise Solution To Exercise 7.10|20 Videos
APPLICATIONS OF INTEGRATION
PREMIERS PUBLISHERS|Exercise Answer the following questions.|18 Videos

Similar Questions

Explore conceptually related problems

The statement ''If f has a local extremum at c and if f'( c) exists then f'( c) = 0'' is __________

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 (a)has a local extermum at x=c dot (b) f has neither local maximum nor minimum at x=c (c) f is necessarily a constant function (d)it is difficult to say whether (a)or(b)dot

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

If the function f(x)=ax e^(-bx) has a local maximum at the point (2,10), then

Let f(x) be a cubic polynomial which has local maximum at x=-1 \ and \ f(x) has a local minimum at x=1. if f(-1)=10 \ and \ f(3)=-22 , then one fourth of the distance between its two horizontal tangents is ____________

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these

Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 less than m less than n Then y=h(x) has a)no local extremums b)one local maximum c)one local minimum d)none of these

L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2 Then at x=1/2, which of the following is/are not true? (a) f has a local maxima (b) f has a local minima (c) f has an inflection point. (d) f has a removable discontinuity.

Draw the graph of the function y=3x^(4)-4x^(3) . Discuss the points of local extremum, inflection and intervals of monotonicity.

If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then

PREMIERS PUBLISHERS-APPLICATIONS OF DIFFERENTIAL CALCULUS-Problems For Practice (Choose the correct answer)

The equation of the tangent to the curve y = (x^(3))/(5) " at " (-1, -...
Text Solution
|
Which of the following is concave down:
Text Solution
|
If f(a) = 2, f'(a) = 1, g(a) = -1, g' (a) = 2. Then underset(x rarr a)...
Text Solution
|
The velocity v of a particle moving along a straight line when at a di...
Text Solution
|
The value of c in Lagrange's mean value theorem for the function f(x) ...
Text Solution
|
The function f(x) = x^(2) is decreasing in
Text Solution
|
y = -e^(x) is
Text Solution
|
If f has a local extremum at a and if f'(a) exists then
Text Solution
|
A spherical snowball is melting in such a way that its volume is decre...
Text Solution
|
f(x) = sqrtx, a = 1, b = 4 find c in Lagrange's mean value theorm:
Text Solution
|
The point of curve y= 2x^(2) - 6x -4 at which the tangent is paral...
Text Solution
|
The curve y = 3e^(x) and y = (a)/(3) e^(-x) intersect orthogonally if ...
Text Solution
|
f'(x) = x^(2) - 5x + 4 then f(x) is decreasing in
Text Solution
|
If the normal to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle t...
Text Solution
|
For the curve x = e^(t) cos t, y = e^(t) sin t the tangent line is par...
Text Solution
|
If y= 6x - x^(3) and x increases at the rate of 5 units/sec the rate o...
Text Solution
|
If the length of the diagonal of a square is increasing at the rate of...
Text Solution
|
The equation of the normal to the curve theta = (1)/(t) " at " (-3, (-...
Text Solution
|
The point of inflection of the curve y = x^(4) is at:
Text Solution
|
The angle between the curve y = e^(mx) and y = e^(-mx) m gt 1 is
Text Solution
|