Question

INSTANT FAN AND MEDAL EASY
For what value of x is the slope of the curve undefined for the graph defined by x = 10 - t^2, y = t^3 - 12t?

Answer 1

The same thing again,
\(\color{#000000}{ \displaystyle \frac{dy}{dx}=\frac{ \displaystyle \frac{dy}{dt} }{ \displaystyle \frac{dx}{dt}} }\)

Answer 2

Alternatively,

\(\color{#000000}{ \displaystyle y'(x)={\rm slope}=\frac{ \displaystyle y'(t) }{ \displaystyle x'(t)} }\)

Answer 3

and as again, you are then to see when is this expression for slope is undefined; for what values of t?

Answer 4

i still have no idea what to do

Answer 5

do you know how to find the derivative wrt to "t" of
x = 10 - t^2
?

Answer 6

*with respect to "t"

Answer 7

Yeah I derived it, but I'm not sure what to do after deriving @phi , thanks for responding.
x'=-2t {+c}
y'=3t^2-12 {+c}

Answer 8

yes, by x' means dx/dt
and y' means dy/dt

slope of a curve with point (x,y) is defined to by dy/dx

Answer 9

slope of a curve with points (x,y) is defined to be dy/dx

Answer 10

in other words, notice that dy/dt * dt/dx = dy/dx
or if you like
\[ \frac{ \frac{dy}{dt} }{\frac{dx}{dt}}= \frac{dy}{dx}= slope \]

Answer 11

Ah, that makes a lot of sense, thank you so much!

Answer 12

btw, there is no additional +c when you take derivatives
that only happens when you integrate

Answer 13

thus the slope is
\[slope= \frac{3t^2 -12}{-2t} \]

Answer 14

-3x^2+12 / 2x , and this would be undefined at x=0 correct

i mean t not x oops

Answer 15

and it will be undefined when t= 0

Answer 16

Thanks a lot!

Answer 17

yes, exactly