Home
Class 12
MATHS
Let f(x) be a differentiable function in...

Let f(x) be a differentiable function in [2,7]. If f(2) = 3 and `f'(x)le5` all x in (2,7) then the maximum possible value of f(x) at x=7 is

A

7

B

15

C

28

D

14

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a differentiable function in [2,7] . If f(2)=3 and f'(x)le5 for all x in (2, 7), then the maximum possible value of f(x) at x = 7 is-

Let f(x)=x^(3)-9x^(2)+30x+5 be a differentiable function of x , then -

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(x to 2) (f(4) -f(x^(2)))/(x-2) equals

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(xrarr2)(f(4)-f(x^2))/(x-2) equals

Let f:[1,oo) → [2, ∞) be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

If f(x) is a differentiable function for all x gt 0 and lim_(y to x)(y^(2)f(x)-x^(2)f(y))/(y-x)=2 , then the value of f'(x) is -

If f is a real- valued differentiable function such that f(x)f'(x) lt 0 for all real x, then

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If x=-1 and x=2 are extreme points of f(x)=alphalog|x|+beta|x|^2+x the...

    Text Solution

    |

  2. For every real number x, f(x)=x/(1!)+3/(2!)x^2+7/(3!)x^3+15/(4!)x^4+...

    Text Solution

    |

  3. Let f(x) be a differentiable function in [2,7]. If f(2) = 3 and f'(x)l...

    Text Solution

    |

  4. Suppose that the equation f(x)=x^2+bx+c has two distinct real roots al...

    Text Solution

    |

  5. Let f(x)=inte^x(x-1)(x-2)dx, then f(x) decreases in the interval

    Text Solution

    |

  6. Let R be the set of all real numbers and f:[1,-1]rarrR be defined by ...

    Text Solution

    |

  7. Suppose that f(x) is a differentiable function such that f'(x) is cont...

    Text Solution

    |

  8. Applying Lagrange's Mean Value Theorem for a suitable function f(x) in...

    Text Solution

    |

  9. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

    Text Solution

    |

  10. The number of points in (-oo,oo) for which x^2-xsinx-cosx=0 is

    Text Solution

    |

  11. If f(x)=|x|+|x-1|+|x-2|, then

    Text Solution

    |

  12. Let f(x)=xsinpix,xgt0 .Then for all natural number n, f'(x) vanishes a...

    Text Solution

    |

  13. The intercepts on x-axis made by tangents to the curve, oversetxunders...

    Text Solution

    |

  14. The real number k of for which the equation 2x^3+3x+k=0 has two distin...

    Text Solution

    |

  15. If y=sec(tan^(-1)x), then value of dy/dx at x=1 is

    Text Solution

    |

  16. If f(x)=e^x(x-2)^2 then

    Text Solution

    |

  17. Let f(x)=sinx+2cos^2x,pi/4lexle(3pi)/4. then f attains its

    Text Solution

    |

  18. Let exp(x) denote exponential function e^x. If f(x)=exp(x^(1/x)).xgt0 ...

    Text Solution

    |

  19. The minimum value of the function f(x)=2|x-1|+|x-2| is

    Text Solution

    |

  20. Let f(x)={(x^2|cos"pi/x|,xne0),(0,x=0):}

    Text Solution

    |