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05:06
04:57Computer Explorations
Use a CAS to perform the following steps in Exercises 55–62.
b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P.
2y² + (xy)¹/³ = x² + 2, P(1,1)
Suppose that functions ƒ(x) and g(x) and their first derivatives have the following values at x = 0 and x = 1.
x ƒ(x) g(x) ƒ'(x) g'(x)
0 1 1 -3 1/2
1 3 5 1/2 -4
Find the first derivatives of the following combinations at the given value of x.
c. ƒ(x) , x = 1
g(x) + 1
Computer Explorations
Use a CAS to perform the following steps in Exercises 55–62.
b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P.
x√(1 + 2y) + y = x², P(1,0)
The folium of Descartes (See Figure 3.27)
c. Find the coordinates of the point A in Figure 3.29 where the folium has a vertical tangent line.
Diagonals If x, y, and z are lengths of the edges of a rectangular box, then the common length of the box’s diagonals is s = √(x² + y² + z²).
b. How is ds/dt related to dy/dt and dz/dt if x is constant?
Area The area A of a triangle with sides of lengths a and b enclosing an angle of measure θ is
A = (1/2) ab sinθ.
b. How is dA/dt related to dθ/dt and da/dt if only b is constant?
