Home
Class 12
MATHS
A twice differentiable function f(x)is d...

A twice differentiable function f(x)is defined for all real numbers and satisfies the following conditions `f(0) = 2; f'(0)--5 and f"(0) = 3`. The function `g(x)` is defined by `g(x) = e^(ax) + f (x) AA x in R`, where 'a' is any constant If `g'(0) + g"(0)=0`. Find the value(s) of 'a'

A

1

B

`-1`

C

2

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|23 Videos
  • COMPOUND ANGLES

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

A function g(x) is defined g(x)=2f((x^(2))/(2))+f(6-x^(2)),AA x in R such f'(x)>0,AA x in R, then mg(x) has

A function defined for all real numbers is defined for x>-0 as follows f(x)={x|x|, 0 =1} How if f defined for x<=0. If (i) f is even ? (ii) f is odd ?

Let f: R to R be any function. Define g : R to R by g(x) = | f(x), AA x . Then, g is

A function f : R to R Satisfies the following conditions (i) f (x) ne 0 AA x in R (ii) f(x +y)= f(x) f(y) AA x, y, in R (iii) f(x) is differentiable (iv ) f'(0) =2 The value of f(0) is

If f and g are two functions defined as f (x) = x + 2, x le 0 , g (x) = 3 , x ge 0, then the domain of f + g is

Let f and g be two real valued functions ,defined by f(x) =x ,g(x)=[x]. Then find the value of f+g

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f and g be differentiable on R and suppose f(0)=g(0) and f'(x) =0. Then show that f(x) =0

If f(x) is an even function and satisfies the relation x^(2)f(x)-2f(1/x)=g(x),xne0 , where g(x) is an odd function, then find the value of f(2).

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If f (x)=|||x|-2|+p| have more than 3 points non-derivability then the...

    Text Solution

    |

  2. Identify the options having correct statement:

    Text Solution

    |

  3. A twice differentiable function f(x)is defined for all real numbers an...

    Text Solution

    |

  4. If f(x) = |sinx|, then

    Text Solution

    |

  5. Let [.] represent the greatest integer function and f (x)=[tan^2 x] th...

    Text Solution

    |

  6. Let f be a differentiable function satisfying f'(x)=f' (-x) AA x in R....

    Text Solution

    |

  7. Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n i...

    Text Solution

    |

  8. Let f (x) =[x] and g (x) =0 when x is an integer and g (x) =x ^(2) whe...

    Text Solution

    |

  9. Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...

    Text Solution

    |

  10. Let f (x) =|2x-9|+|2x+9|. Which of the following are true ?

    Text Solution

    |

  11. Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:

    Text Solution

    |

  12. Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA, x...

    Text Solution

    |

  13. Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...

    Text Solution

    |

  14. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

    Text Solution

    |

  15. If y =e ^(x sin (x ^(3)))+(tan x)^(x) then (dy)/(dx) may be equal to:

    Text Solution

    |

  16. Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...

    Text Solution

    |

  17. Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...

    Text Solution

    |

  18. If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...

    Text Solution

    |

  19. If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...

    Text Solution

    |

  20. Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)...

    Text Solution

    |