# math

Find the slope m of the tangent to the curve
y = 5/ sqrt (x) at the point where
x = a > 0.
what is the slope?

1. 👍
2. 👎
3. 👁
1. y = 5x^(-1/2)
dy/dx = (-5/2)x^(-3/2)

so when x=a

slope = (-5/2)x^(-3/2)

1. 👍
2. 👎

1. 👍
2. 👎
3. -5/(a)(2 sqrt a)

1. 👍
2. 👎
4. -5/2a^3/2

1. 👍
2. 👎
5. WRONG

1. 👍
2. 👎

## Similar Questions

1. ### calculus

The point P(7, −4) lies on the curve y = 4/(6 − x). (a) If Q is the point (x, 4/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9

Given the curve x^2-xy+y^2=9 A) write a general expression for the slope of the curve. B) find the coordinates of the points on the curve where the tangents are vertical C) at the point (0,3) find the rate of change in the slope

3. ### Calculus

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

4. ### Calc AB

Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to

1. ### Calculus

The curve y = x/(1 + x^2) is called a serpentine. Find an equation of the tangent line to this curve at the point(2, 0.40).(Round the slope and y-intercept to two decimal places.)

2. ### calculus

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this

3. ### Equation of the Tangent Line

Find the equation of a line tangent to te curve xy = sqrt(xy - x) + 1 at the point (1, 2).

4. ### Calculus

Suppose that y=f(x) = sqrt(2x), x>=0 Find a c > 0 such that the tangent line to the curve y = f(x) at x = c has the same slope as the tangent line to the curve y = f^–1(x) at x = c. You get: c = 1/8 c = 1/2 c = (1/8)^(1/3) c =

1. ### Math

using first principle, find the slope of a tangent line to the curve f(x) = x^2-3x+5 at x=3

2. ### Calculus

A) The point p(3,1) lies on the curve y= square root x-2. If Q is the point (x, square root x-2) use your calculator to find the slope of the decant line PQ for the following values of x 1) 2.5 2.) 2.9 3.) 2.99 4.) 2.999 5.) 3.5

3. ### Calculus

Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line

4. ### calculus

Find an equation of the tangent to the curve f(x) = 2x^2 - 2x + 1 that has slope 2.