Determine the values of x for which the function f(x) = x2 6x + 9 is increasing or - Maths -

Question

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

Global Expert · Accepted Answer

Here,fx=x2-6x+9f'x=2x-6For f(x) to be increasing, we must havef'x>0⇒2x-6>0⇒2x>6⇒x>3⇒x∈3, ∞So, f(x) is increasing on 3, ∞ For f(x) to be decreasing, we must havef'x<0⇒2x-6<0⇒2x<6⇒x<3⇒x∈-∞, 3So, f(x) is decreasing on -∞, 3 Let (x, y) be the coordinates on the given curve where the normal to the curve is parallel to the given line Slope of the given line = 1 Slope of tangent = dydxx, y= 2x-6Slope of normal = -1Slope of tangent=-12x-6Now,Slope of normal = Slope of the given line-12x-6=1-1=2x-62x=5x=52Given curve isy=x2-6x+9 =254-15+9 =14x, y=52, 14Hence, the coordinates are 52, 14

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.