A point moves along the graph y= x^(5/2) so that its x coordinate increases at the constant rate of 2units/second. Find the rate at which its y coordinate is increasing as it passes the point (4 ,32)?

Question

1111 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-26T14:12:57

#dy/dt = 40# (#y#-units)/second

If #y= x^(5/2)#

and #dx/dt = 2# (#x#-units)/second.

find #dy/dt# when #x=4# (and #y=32#).

Differentiate #y= x^(5/2)# with respect to #t# (use implicit differentiation):

#dy/dt= 5/2x^(3/2) dx/dt#

Substitue the known value for #x# and #dx/dt# and solve for #dy/dt#:

#dy/dt= 5/2x^(3/2) dx/dt#

# = 5/2(4)^(3/2) (2)#

# = 40#