wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5.

Open in App
Solution

Here,fx=x2-6x+9f'x=2x-6For f(x) to be increasing, we must havef'x>02x-6>02x>6x>3x3, So, f(x) is increasing on 3, .For f(x) to be decreasing, we must havef'x<02x-6<02x<6x<3x-, 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.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Direction Cosines and Direction Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon