Home
Class 12
MATHS
A continuous and differentiable function...

A continuous and differentiable function `y=f(x)` is such that its graph cuts line `y=m x+c` at `n` distinct points. Then the minimum number of points at which `f^('')(x)=0` is/are `n-1` (b) `n-3` (c) `n-2` (d) cannot say

A

`n-1`

B

`n-3`

C

`n-2`

D

cannot say

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

A continuous and differentiable function y=f(x) is such that its graph cuts line y=m x+c at n distinct points. Then the minimum number of points at which f''(x)=0 is/are (a) n-1 (b) n-3 (c) n-2 (d) cannot say

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in [0,1]for which f^(prime)(c)(f(c))^(n-1)>sqrt(2^(n-1)) , where n in Ndot

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < de, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))+1)^(n) is (a) 2n (b) 3n (c) 2n+1 (d) 3n+1

Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y/b=2 at the point (a,b), whatever be the value of n.

A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It its graph passes through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is 1 (b) -1 (c) 2 (d) 0

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. In which of the following function Rolle's theorem is applicable ?

    Text Solution

    |

  2. Let f^(prime)(x)=e^x^2 and f(0)=10. If A< f(1)< B can be concluded fro...

    Text Solution

    |

  3. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

    Text Solution

    |

  4. A continuous and differentiable function y=f(x) is such that its graph...

    Text Solution

    |

  5. A man 2m tall, walks at the rate of 1 2/3m//s e c towards a street lig...

    Text Solution

    |

  6. A man 2m tall, walks at the rate of 1 2/3m//s e c towards a street lig...

    Text Solution

    |

  7. Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an...

    Text Solution

    |

  8. For the curve y=ce^(x//a) , which one of the following is incorrect?

    Text Solution

    |

  9. Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the poi...

    Text Solution

    |

  10. The angle formed by the positive y-a xi s and the tangent to y=x^2+4x-...

    Text Solution

    |

  11. Which of the following pair(s) of curves is/are ortogonal? (a) ...

    Text Solution

    |

  12. The coordinates of the point(s) on the graph of the function f(x)=(x^3...

    Text Solution

    |

  13. The abscissa of a point on the curve x y=(a+x)^2, the normal which cut...

    Text Solution

    |

  14. The angle between the tangents at any point P and the line joining P t...

    Text Solution

    |

  15. If OT and ON are perpendiculars dropped from the origin to the tangent...

    Text Solution

    |

  16. Let C(1):y=x^(2)sin3x,C(2):y=x^(2)and C(3):y=-y^(2), then

    Text Solution

    |

  17. If the line x cos theta+y sin theta=P is the normal to the curve (x+a)...

    Text Solution

    |

  18. Common tagent (s) to y=x^(3)and x=y^(3) is/are

    Text Solution

    |

  19. Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 h(x)={x},k(...

    Text Solution

    |

  20. Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , where ai ' s are real and f(x)=...

    Text Solution

    |