Question

Determine the slope of the curve defined by the equation:
(attached below)

Answer 1

hmmm, the equation there is already the derivative, so to find the slope just set x = -10

4(-1)-2

Answer 2

bleh, 4(-10)-2

Answer 3

It is asking for the slope of the curve
f(x) = 4x -2
or

y = 4x -2

this is the equation of a line, and lines have constant slope (unlike say a parabola)
so the slope at any x is the same number.

what is the slope of a line (notice this equation is in the form y = mx + b)

Answer 4

i did

Answer 5

when 4(-10)+(-2)= -42

Answer 6

of course, you could use calculus
and take the derivative of both sides

\[ \frac{dy}{dx} = 4 \]

Answer 7

excuse me?

Answer 8

hmmm, I read "this is the slope define by this equation" hehehh

Answer 9

oh okay

Answer 10

the question says

determine the slope of the curve defined by the equation...

in other words, the equation defines a curve (line in this case)

Answer 11

so i plugged in -10 into x

Answer 12

right.

Answer 13

hmm, i see, the equation is defining the curve, no the slope heh

Answer 14

you have
y = 4x-2

plugging in x with a number gives you the y value

but you want the slope ... you want dy/dx

Answer 15

if this is confusing, see
http://www.khanacademy.org/math/calculus/differential-calculus/derivative_intro/v/calculus--derivatives-1--new-hd-version

Answer 16

how do we know to use derivative and not just plug in -10 into x

Answer 17

notice that for this problem, you don't need calculus
the slope of a line in the form y = mx +b is m (the coefficient of x)

Answer 18

im sort of confused

Answer 19

see the video. it is most excellent

Answer 20

okie

Answer 21

are you sure?

Answer 22

hmm, I was noticing that, 4x-2 is just a line, nothing curvy about it

Answer 23

do we use lim delta x

Answer 24

etc etc?

Answer 25

isn't x=-10 and y=-42?

Answer 26

the slope of this line is 4 (no matter what x is)

so the answer is 4

Answer 27

so can we do this problem together?

Answer 28

there are other formulas im confused with

Answer 29

@phil

Answer 30

@phi

Answer 31

what is the question ?

Answer 32

i got the answer.

Answer 33

4

Answer 34

however, to do this i had to use this : f(x+deltax)-f(x)/delta x

Answer 35

why?

Answer 36

i didnt have to plug in -10 into x

Answer 37

is this: f(x+deltax)-f(x)/delta x the same as f(b)-f(a)/ b-a?

Answer 38

yes, it is the same idea. we set b= a + delta x (b is just a little bigger than a