Home
Class 12
MATHS
What is the minimum height of any point ...

What is the minimum height of any point on the curve `y=x^2+6x-5` above the x-axisdv?

Text Solution

Verified by Experts

`y = -x^(2) + 6x - 5`
`=4- (x -3)^(2)`
Now `(x - 3)^(2) ge 0` for all real x,
Hence, the maximum value of `y(or - x^(2) + 6x - 5) ` is 4, which is the maximum height of the graph above x-axis.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

What is the minimum height of any point on the curve y=x^(2)-4x+6 above the x -axis?

The minimum distance of a point on the curve y=x^2-4 from origin ,

The minimum distance of a point on the curve y=x^(2)-4 from the origin is :

Any tangent to the curve y=3x^(7)+5x+3

Determine the values of x for which the function f(x)=x^(2)-6x+9 is increasing,or decreasing.Also,find the coordinates of the point on the curve y=x^(2)-6x+9 where the normal is parallel to the line y=x+5

Determine the values of x for which the function f(x)=x^(2)-6x+9 is increasing or decreasing.Also,find the coordinates of the point on the curve y=x^(2)-6x+9 where the normal is parallel to the line y=x+5 .

If tangen at any point of the curve y=x^3+lamdax^2+x+5 makes acute angle with x-axis then

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is -

The length of the subtangent at any point (x_1,y_1) on the curve y=5^x is

CENGAGE-THEORY OF EQUATIONS-Examples
  1. If x-c is a factor of order m of the polynomial f(x) of degree n(1<m<n...

    Text Solution

    |

  2. What is the minimum height of any point on the curve y=x^2-4x+6 above ...

    Text Solution

    |

  3. What is the minimum height of any point on the curve y=x^2+6x-5 above ...

    Text Solution

    |

  4. Find the largest natural number a for which the maximum value of f(x)=...

    Text Solution

    |

  5. Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3...

    Text Solution

    |

  6. Find the least value of n such that (n-2)x^2+x+n+4>0,AAx in R ,w h e ...

    Text Solution

    |

  7. Given that a ,b ,c are distinct real numbers such that expressions a x...

    Text Solution

    |

  8. For a in R, if |x - a + 3| + |x-3a|=2x - 4a +3 | is ture AA x inR. T...

    Text Solution

    |

  9. If c is positive and 2a x^2+3b x+5c=0 does not have aby real roots, th...

    Text Solution

    |

  10. If a x^2+b x=6=0 does not have distinct real roots, then find the leas...

    Text Solution

    |

  11. A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=...

    Text Solution

    |

  12. If the inequality (m x^2+3x+4+2x)//(x^2+2x+2)<5 is satisfied for all x...

    Text Solution

    |

  13. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  14. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

    Text Solution

    |

  15. Let x^(2) - ( m - 3) x + m = 0 ( m in R) be a quadratic equation. Find...

    Text Solution

    |

  16. If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbe...

    Text Solution

    |

  17. The equation a x^2-b x+c=0 has real and positive roots. Prove that the...

    Text Solution

    |

  18. For what real values of a do the roots of the equation x^2-2x-(a^2-1)=...

    Text Solution

    |

  19. If (x^2+x=2)62=(a-3)(x^2+x+1)(x^2+x+2)+(a-4)(x^2+x+1)^2=0 has at least...

    Text Solution

    |

  20. Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 ...

    Text Solution

    |