The smallest value of x^2 - 3x + 3 in the int | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $f(x) = x^2 - 3x + 3$. Completing the square,we get $f(x) = (x - 3/2)^2 + 3/4$. The vertex of the parabola is at $x = 3/2$. Since the interval

Vedclass · Accepted Answer

$3/4$

Vedclass · Answer

(A) Let $f(x) = x^2 - 3x + 3$. Completing the square,we get $f(x) = (x - 3/2)^2 + 3/4$. The vertex of the parabola is at $x = 3/2$. Since the interval is $(-3, 3/2)$,the function $f(x)$ is strictly decreasing on this interval. As $x$ approaches $3/2$ from the left,$f(x)$ approaches $3/4$. Since $3/2$ is not included in the interval,the function does not attain the value $3/4$,but it is the infimum (greatest lower bound) of the function on this interval.

The smallest value of $x^2 - 3x + 3$ in the interval $(-3, 3/2)$ is

Similar Questions

Let $P$ be a point on the parabola $x^2 = 4y$. If the distance of $P$ from the centre of the circle $x^2 + y^2 + 6x + 8 = 0$ is minimum,then the equation of the tangent to the parabola at $P$ is:

What is the equation of the pair of tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 12x$?

If the coordinates of the ends of a focal chord of the parabola $x^2=4ay$ are $(x_1, y_1)$ and $(x_2, y_2)$,then

Which one of the following equations,represented parametrically,represents a parabolic profile?

The maximum number of common normals of $y^2=4ax$ and $x^2=4by$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module