Question

find the the rate of change dy/dx
where x=x0

Answer 1

\[y=-17; x _{0}=3\]

Answer 2

If the function is the constant function y = -17, then the derivative of it (dy/dx) is simply 0.

The derivative of any constant is "0". Remember that "derivative" means "the change y with respect to x" in this case. If y = -7 at all points, then it never changes with respect to x. Therefore, the change is 0.

Answer 3

so what do you do with the 3

Answer 4

there has to be more to this question which you have not given us

Answer 5

if the equation for y is simply: y = -17 .. then daru is correct.

Answer 6

sorry wrong problem
\[y=6-2x; x_{0}=3\]

Answer 7

?

Answer 8

first step, is to take the derivative of y, but the method of that step differs depending on how youre spose to go about it.

there is a first principals method, and the derivative rules method. Which method have you been doing in your lessons?

Answer 9

both

Answer 10

derivative rules are much easier to work with then; what derivative rule would you say can apply to this question?

Answer 11

wouldn't the derivative be 2

Answer 12

almost, that negative sign (subtraction) needs to be recognized :)

y= 6 - 2x
y' = 6' - (2x)'
= 0 - 2

Answer 13

now, since there is no place to plug in the value of x in the derivative; the value of the derivative at ANY point is: -2

Answer 14

oh ok.

Answer 15

/so how do you find that slope of tangent after taking the derivative?

Answer 16

the value of the derivative DEFINES the slope of the tangent at a given point.

Answer 17

in this case, 6 - 2x is a straight line whose sloe is -2 at all points

Answer 18

so in a problem such as f(x)=5x-3
the slope of the line that is tangent is 5?

Answer 19

yes

Answer 20

the more complicated the curve, the less trivial the derivative becomes :)

take: y=x^2
y' = 2x

the slope at any given point of y=x^2 is defined as 2x

the slope at x=3 would be 2(3) = 6
the slope at x=7 would be 2(7) = 14
the slope at x=-2 would be 2(-2) = -4

Answer 21

ok. thanks