# Calculus

posted by Caleb

Use implicit differentiation to find an equation
of the tangent line to the curve
y^2 = x^3 (26 − x)
at the point (1, 5).

1. Damon

2 y dy = x^3(-dx)+3x^2dx(26-x)

2 y dy = -x^3 dx + 78 x^2 dx - 3 x^3 dx

dy/dx = (-4 x^3 + 78 x^2)/ (2 y)

dy/dx = m = (39 x^2 - 2 x^3)/y
at (1,5)
m = (39-2)/5 = 37/5

so y = (37/5) x + b
5 = 37/5 + b
b = 25/5 - 37/5 = -12/5
so
y = (37/5) x - 12/5
5 y = 37 x - 12

## Similar Questions

1. ### math calculus

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31). The equation of this tangent line can be written in the form y=mx+b where m is
2. ### Calculus

Use implicit differentiation to find an equation of the tangent line to the curve y^2 = x^3 (26 − x) at the point (1, 5).
3. ### COLLEGE CALCULUS.

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=5 at the point (4,1) . The equation of this tangent line can be written in the form y = mx+b where m is:?
4. ### calculus

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy − y2 + x = 17, (3, 5) (hyperbola)
5. ### calculus

use implicit differentiation to find an equation of the tangent line to the curve at the given point. 9x^2+xy+9y^2=19, (1,1) (ellipse)
6. ### Calculus

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x^2 + xy + y^2 = 3, (1,1)
7. ### Calculus

Use implicit differentiation to find an equation of the tangent line to the graph at the given point. x + y − 1 = ln(x^5 + y^5), (1, 0)
8. ### Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+4y^2−x)^2 (0, 0.25) (cardioid)
9. ### Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2/3 +y^2/3 =4 (-3sqrt(3),1) (astroid)
10. ### calculus

Use implicit differentiation to find an equation of the tangent line to the curve 3xy^3+4xy=63 at the point (9,1)(9,1).

More Similar Questions