Question

Help...
Find the slope of tangent line
x(t)= sqrt(t), y(t) = (1/4)(t^2 -4), t>0
Answer: 8
I have no clue....

Answer 1

are u given a "point" at which u want the slope of tangent line ?

Answer 2

no. That is literally the entire question...

Answer 3

first calculate dy/dt and dx/dt
now calculate dy/dx by (dy/dt)/(dx/dt) this is the slope

Answer 4

or eliminate t and find y as a function of x then differentiate it.

Answer 5

i like that way if you are able to do it

Answer 6

But how is the answer 8??

Answer 7

no it;s function of x or t for any number you have to know specific point where tangent asked.

Answer 8

so if I eliminate t between x and y I would get the same answer as if I tool dy/dx right?

Answer 9

I feel like I am missing something because elimination gets me x^3 and dy/dx gets me t(sqrt(t))

Answer 10

after eliminate t you gate equation of curve as y= f(x) now you have to find dy/dx.

Answer 11

tsqrt(t) = x^2sqrt(x^2) = x^2.x = x^3

Answer 12

so nthng to confuse okay

Answer 13

so now what's missing is the point huh?

Answer 14

obviously ! slope is not a constant, so u wont get 8 as answer unless u r a given a point

Answer 15

x(t)= sqrt(t), y(t) = (1/4)(t^2 -4),
square first you get t= x^2 now put this value of t in second you will get y= function of x

Answer 16

My professor is too old then to forget to put a point then. Thanks guys. Appreciate it.

Answer 17

lol thats funny ;)

Answer 18

u wlc !

Answer 19

A point technically is not needed to find the slope of the mutual tangent lines.

Answer 20

do you know how to get 8 then?