146k views
3 votes
find (a) the slope of the curve at the given point p, and (b) an equation of the tangent line at p. y= 1/x; p(5,1/5)

User Kasperd
by
7.7k points

1 Answer

2 votes

Answer:

(a) -1/25

(b) y = -1/25x +2/5

Explanation:

You want the slope and tangent line equation for the curve y = 1/x at point P(5, 1/5).

(a) Slope

The slope is the derivative of the function at the given point:

y = 1/x = x^(-1)

y' = (-1)x^(-1-1) = -1/x²

At x=5, the slope is ...

m = -1/5² = -1/25

(b) Equation

The equation of the tangent line is conveniently written using slope-intercept form:

y -k = m(x -h) . . . . . . . . equation for line with slope m at point (h, k)

y -1/5 = -1/25(x -5) . . . . equation for line with slope -1/25 at point (5, 1/5)

Rearranging, we have the slope-intercept form ...

y = -1/25x +2/5

<95141404393>

find (a) the slope of the curve at the given point p, and (b) an equation of the tangent-example-1
User Apieceofbart
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories