Question

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)

Answer 1

(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

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