Question

The expression dy/dx = x(3√y) gives the slope at any point on the graph of the function f(x) where f(2) = 8.

Answer 1

A. Write the equation of the tangent line to f(x) at point (2, 8).
B. Write an expression for f(x) in terms of x.
C.What is the domain of f(x)?
D. What is the minimum value of f(x)?
E. Using the axes provided, sketch a slope field for the given differential equation at the nine points indicated.

Answer 2

@welshfella

Answer 3

@phi

Answer 4

A:- substitute the values of m ( = dy/dx) and the point (2,8) in the standard form

y - y1 = m(x - x1)


x1 = 2 and y1 = 8

NOte also :- x = 2 and y =8 for dy/dx

Answer 5

So are you saying the equation is y-8= m(x-2)?

Answer 6

@welshfella

Answer 7

yes but you can work out the slope m from the info given

m = dy/dx

Answer 8

m=8/2 = 4?

Answer 9

plug in x =2 and y = 8 into dy/dx

Answer 10

dy/dx = 2(3sqrt8)

Answer 11

that = m in the dtandard equation

Answer 12

so we get y-8 = 2(3sqrt8)(x-2)

Answer 13

yes but
we could simplify it a bit

y = 6sqrt8 (x - 2) + 8

Answer 14

Alright that makes sense.

Answer 15

sorry gotta go right now

Answer 16

That's fine. You helped me with the first part.

Answer 17

@rational can you pick up where he left off?

Answer 18

@jigglypuff314 could you pickup where he left off?