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Derivative of even function is...

Derivative of even function is

A

non-negative

B

even function

C

odd function

D

zero

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The correct Answer is:
B
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Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(h to 0^(+))(f(a)-f(a-h))/(h) =lim_(hto0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(h to 0^+)(f(a+h)-f(a))/(h) =lim_(hto0^(+))(f(a)-f(a+h))/(h) =lim_(hto0^(+))(f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. The statement lim_(hto0)(f(-x)-f(-x-h))/(h)=lim_(hto0)(f(x)-f(x-h))/(-h) implies that for all x"inR ,

The derivative of an even function is always an odd function.

Prove that the derivative of an even function is an odd function and that of an odd function is an even function.

Derivative of odd function is

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Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

NIKITA PUBLICATION-DIFFERENTIATION -MCQ
  1. If f is derivable at x =a,then lim(xto a )( (xf(a) -af( x))/(x-a) )

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  2. If the relation f'(a+b) =f'( a)+ f '(b) and (d)/(dx)(f(x))=f'(x) ,the...

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  3. Derivative of even function is

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  4. Derivative of odd function is

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  5. If f (x) is polynomial of degree two and f(0) =4 f'(0) =3,f''(0) =4,th...

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  6. If f (x) is a polynomial of degree two and f(0) =4 f'(0) =3,f'' (0) 4 ...

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  7. let f(x) be a polynomial function of second degree. If f(1)=f(-1)and a...

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  8. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

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  10. If y = (1)/( (x^(2) +3)) , then (dy)/(dx) =

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  11. If y= sqrt (x+(1)/( x) ),then (dy)/(dx) =

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  12. If y= (sqrt( x) +(1)/(sqrt(x)) ) ^(5) , then (dy)/(dx) =

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  13. If y= 3sqrt ((2x^(2) -7x -4) ^(5) ) ,then (dy)/(dx) =

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  14. If y= sqrt (x+ sqrt (x+ sqrt (x))),then (dy)/(dx) =

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  15. If y=sqrt((1-x)/(1+x)), then (1-x^(2))(dy)/(dx)+y is equal to

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  16. If y= (1)/(sqrt( 3x+ 7) )- (1)/(sqrt(7-3x) ),then (dy)/(dx) =

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  17. If y= 1+x+ (x^(2)) /(2!) +(x^(3))/( 3!) +......infty ,then (dy)/(dx)...

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  18. If y = (1)/(1+x^( p-r) +x^(q-r)) +(1)/( 1+ x^(p-q) +x^(r-q) )+ (1) /( ...

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  19. If y =sqrt(a^(2) + sqrt( a^(2)+ x^(2)) ),then (dy)/(dx) =

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  20. If y =sin (x^(2) +x) ,then (dy)/(dx) =

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