The function f is defined as f(x)=2x+3. What is the x-coordinate of the point on the function's graph that is closest to the origin?

Question

The function  f is defined as  f(x)=2x+3. What is the  x-coordinate of the point on the function's graph that is closest to the origin?

Bytelearn · Accepted Answer

Define Distance Formula: To find the point closest to the origin, we need to minimize the distance from the point (x, f(x)) to the origin (0,0). The distance formula is D = √((x-0)² + (f(x)-0)²).Substitute f(x): Substitute f(x) with 2x+3 to get the distance in terms of x: D = √(x² + (2x+3)²).Simplify Distance Formula: Now we have D = √(x² + (4x² + 12x + 9)), which simplifies to D = √(5x² + 12x + 9).Minimize Distance: To find the minimum distance, we can take the derivative of D with respect to x and set it to zero. But since D is always positive, we can minimize D² for simplicity. So we'll minimize 5x² + 12x + 9.Find Derivative: The derivative of 5x² + 12x + 9 with respect to x is 10x + 12.Set Derivative Equal: Set the derivative equal to zero to find the critical point: 10x + 12 = 0.Solve for x: Solve for x: 10x = -12.Simplify Fraction: Divide by 10: x = -12/10.Simplify the fraction: x = -6/5 or x = -1.2.

The function $f$ is defined as $f(x)=2 x+3$ . $\newline$ What is the $x$ -coordinate of the point on the function's graph that is closest to the origin?

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The function f f f is defined as f(x)=2x+3 f(x)=2 x+3 f(x)=2x+3.\newlineWhat is the x x x-coordinate of the point on the function's graph that is closest to the origin?

The function $f$ is defined as $f(x)=2 x+3$ . $\newline$ What is the $x$ -coordinate of the point on the function's graph that is closest to the origin?