Home
Class 12
MATHS
Suppose f(x)=e^(ax)+e^(bx)," where " a n...

Suppose `f(x)=e^(ax)+e^(bx)," where " a ne b,` and that f''(x) -2f'(x)-15f(x)=0 for all x. Then the product ab is

A

25

B

9

C

-15

D

-9

Text Solution

Verified by Experts

`(a^(2)-2a-15)e^(ax)+(b^(2)-2b-15)e^(bx)=0`
`"or "(a^(2)-2a-15)=0 and b^(2)-2b-15=0`
`"or "(a-5)(a+3)=0 and (b-5)(b+3)=0`
`i.e., a=5 or -3 and b=5 or -3`
`therefore" "aneb`
Hence, `a=5 and b=-3 or a =-3 and b=5`
`"or "ab=-15`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|24 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Suppose f(x)=e^(ax)+e^(bx), where aneb and f''(x)-2f'(x)-15f(x)=0 for all x, then the value of |a+b| is equal to......

Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f''(x)-2f^(prime)(x)-15f(x)=0 for all xdot Then the value of (|a b|)/3 is ___

Suppose f(x)=e^(ax) + e^(bx) , where a!=b , and that fprimeprime(x)-2fprime(x)-15f(x)=0 for all x . Then the value of ab is equal to:

f(x)=e^x-e^(-x) then find f'(x)

If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If y=f(x)=(ax-b)/(bx-a) , the prove that : x=f(y)

Suppose f(x) =[a+b x , x 1] and lim f(x) where x tends to 1 f(x) = f(1) then value of a and b?

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

CENGAGE ENGLISH-DIFFERENTIATION-Execrises
  1. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  2. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  3. Suppose f(x)=e^(ax)+e^(bx)," where " a ne b, and that f''(x) -2f'(x)-1...

    Text Solution

    |

  4. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a l to a)2^(20)(cos2x-2^(20)o...

    Text Solution

    |

  5. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

    Text Solution

    |

  6. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

    Text Solution

    |

  7. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |

  8. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

    Text Solution

    |

  9. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

    Text Solution

    |

  10. A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, wher...

    Text Solution

    |

  11. Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...

    Text Solution

    |

  12. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

    Text Solution

    |

  13. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

    Text Solution

    |

  14. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  15. Let y=ln (1+ cos x)^(2). The the value of (d^(2)y)/(dx^(2))+(2)/(e^(y/...

    Text Solution

    |

  16. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...

    Text Solution

    |

  17. "Let "y=t^(10)+1 and x=t^(8)+1." Then "(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  18. If x = log p and y=(1)/(p), then

    Text Solution

    |

  19. If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...

    Text Solution

    |

  20. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

    Text Solution

    |