If f(x)={{:(x+2, -1 lt x lt 3), (5, x=3)...

If `f(x)={{:(x+2, -1 lt x lt 3), (5, x=3), (8-x, x gt 3):}`, then at x=3, `f'(x)` is

`-1`

does not exist

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION
FULL MARKS|Exercise EXERCISE 5 ADDITIONAL PROBLEMS|4 Videos
DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION
FULL MARKS|Exercise EXERCISE 5 ADDITIONAL PROBLEMS (Find the derivative of following functions.)|10 Videos
DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION
FULL MARKS|Exercise EXERCISE 4 (Differentiate the following)|28 Videos
COMBINATORICS AND MATHEMATICAL INDUCTION
FULL MARKS|Exercise ADDITIONAL QUESTIONS|33 Videos
DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY
FULL MARKS|Exercise EXERCISE 9.6|25 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):} , then which one of the following is true?

If the function f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} then the number of roots of the equation f(g(x))=2

If the function f : R to R is defined by f(x)={{:(2x+7","x lt -2),(x^(2)-2","-2 le x lt 3","),(3x-2","x ge 3):} then find the values of (i) f(4) (ii) f(-2) (iii) f(4)+2f(1) (iv) (f(1)-3f(4))/(f(-3))

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

If the p.d.f. f(x)={{:(x/2",", 0 lt x lt 2), (0",", "elsewhere"):} then E(3x^(2)-2x)= ________.

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The domain of the function f(g(x)) is

If the function f: R to R is defined by f (x) {:{( 2x+1 ,xlt-1) ,( x^(2) -1,le x lt 3 ),( 3x-2, xge 3) :} "Find " (f(-1) +f(3))/( 2)

A function f (-3 , 7) to R is defined as follows f (x) = {{:( 4 x^(2) + 1 , ,-3 le x lt 2) , (3x - 2 , ,2 le x le 4) , (2x + 3 , ,4 lt x lt 7):}} Find (i) 5 f(1) - 3 f(-2) (ii) 3f (-3) + 4 f (iii) (7 f (3) - f (-1))/(2 f (6) - f(1))

FULL MARKS-DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 5 (Choose the correct or the most suitable answer from the given four alternatives.)

If y = cos ( sin x^2), then (dy)/(dx) at x= sqrt(pi)/(2) is …...........
Text Solution
|
If y = mx + c and f(0) = f'(0) =1, then f(2) is …......... .
Text Solution
|
If f(x)=xtan^(-1)x, then f'(1) is
Text Solution
|
(d)/(dx) (e^(x + 5 log x)) is …........... .
Text Solution
|
If the derivative of (ax - 5)e^(3x) at x=0 is -13, then the value of a...
Text Solution
|
x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is
Text Solution
|
If x= a sin theta and y =b cos theta, then (d^2 y)/(dx^2) is…............
Text Solution
|
The differential coefficient of log(m) x with respect to log(x) m is …...
Text Solution
|
If f(x) = x+2, then f'(f(x) ) at x=-4 is…......... .
Text Solution
|
If y = ((1-x)^2)/(x^2), then (dy)/(dx) is…........ .
Text Solution
|
If pv = 81, then (dp)/(dv) at v=9 is …............. .
Text Solution
|
If f(x) = {{:(x-5, "if" , x le 1),(4x^2-9, "if", 1 lt x lt 2),(3x+4 ,"...
Text Solution
|
It is given that f'(a) exists, then underset(x to a) (lim) (x f(a) - a...
Text Solution
|
If f(x) = {{:(x+1, "when" , x lt 2),(2x-1, "when" ,x ge 2):}, then f'(...
Text Solution
|
If g(x) = (x^2 + 2x +3) f(x) and f(0) = 5 and underset( x to 0) (lim) ...
Text Solution
|
If f(x)={{:(x+2, -1 lt x lt 3), (5, x=3), (8-x, x gt 3):}, then at x=3...
Text Solution
|
The derivative of f(x) = x |x| at x=-3 is …............ .
Text Solution
|
If f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):}, then...
Text Solution
|
If f(x) = {{:(ax^2 -b",", -1 lt x lt 1),((1)/(|x|)",", "elsewhere"):} ...
Text Solution
|
The number of points in RR in which the function f(x) = |x-1| + sin x ...
Text Solution
|