If the tangent to the curve f(x) = x^2 - 2x + 2 is perpendicular to the straight line 4y - x - 5 = 0, find the coordinates of the point of tangency.
Expert Answers
Tushar Chandra
| Certified Educator
| Certified Educator
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
The first derivative of a curve at any point gives the slope of the tangent at that point.
Here the curve is defined by f(x) = x^2 - 2x + 2
f'(x) = 2x - 2
As the tangent is perpendicular to the the line 4y - x - 5 = 0, it has a slope that is the negative reciprocal of the slope of the line.
4y - x - 5 = 0
=> y = x/4 + 5/4
The slope of the line is 1/4. The slope of the tangent is -4
So 2x - 2 = -4
=> 2x = -2
=> x = -1
For x = -1, f(x) = (-1)^2 + 2 + 2 = 5
Therefore the coordinates of the tangential point are (-1,5)
Related Questions
- What is the area of the region enclosed between the curves y=x^2-2x+2 and -x^2+6 ?
- 1 Educator Answer
- Calculate area bounded by the curve y=cosx/(sin^2x-4), x axis and the lines x = 0 and x = pi/2 .
- 1 Educator Answer
- Evaluate the limit of the function (2x-sin2x)/x^3; x-->0.
- 1 Educator Answer
- y= Arcsin^2x-2x+2√1-x^2 Arcsin X
- 1 Educator Answer
- A curve has dy/dx=3x^2-2x. The curve passes through the point (2;5). What is the equation of the...
- 1 Educator Answer