Mathematical Methods - Pre-Exam 2 Advice for 2012

[Phy124]

Is writing y - f(x1) = m(x - x1) appropriate?

f(x) - f(x₁) = m(x - x₁)

or

f(x) - f(x₁) = f'(x₁)(x - x₁)

or

y - y₁ = m(x - x₁)

Don't have both y(x) and f(x) related notion in the one equation.

[Hutchoo]

If they give you an equation of like f(x) = sqrt (2x-1) and the ask you to find the derivative, can you say
"Let dy/dx = f'(x)" or do you have to say something more like "Let y = f(x) , therefore, dy/dx = f'(x)"?
Just curious about this notation.

[BubbleWrapMan]

I would lean towards the latter, but you might as well just write "f'(x) = ___" straight away. Depends on the question though, I guess. But yes, you do have to define y in order to call something dy/dx, at least in methods situations.

[daniel034]

if its just an expression and not an equation can you right d/dx or is that calculator syntax?

[BubbleWrapMan]

If you mean something like then yes it's fine

[daniel034]

say if the question is find the derivative of x^2 is it acceptable to write d/dx = 2x

[Phy124]

You say

Or if the original equation was , you can say

[BubbleWrapMan]

Yeah, d/dx by itself is meaningless

[paulsterio]

Yeah, d/dx by itself is meaningless

It's an operator that says "differentiate"

So if it's just d/dx by itself, it would just read "differentiate..." which makes no sense.

d(x^2)/dx would mean "differentiate x^2" - which is 2x

[charmanderp]

I would lean towards the latter, but you might as well just write "f'(x) = ___" straight away. Depends on the question though, I guess. But yes, you do have to define y in order to call something dy/dx, at least in methods situations.

So if the question says 'Find the derivative of 2x' in our first line we can write f(x) = 2x and then write in our second line f'(x) = 2?

[BubbleWrapMan]

There's a few ways to do it, quickest way is

But yes that's fine, though you should probably have the word 'Let' in front of the first line

[ldee]

Finding f(x) given f'(x) - a shortcut
- If we know a derivative and a point on the curve f(x), there is a shortcut to solving it
- It's using a command on the CAS called dSolve - for the ClassPad
- Go interactive, advanced, dSolve
- In the first column, type y'=...(derivative)...
- Independent Variable - x
- Dependent Variable - y
- Initial condition, type, for example if we had the point (1, 5) - "x=1,y=5"

Could somebody please give an example as to where to implement this, and what I would input? Can't seem to get it to work.

[link125]

Finding f(x) given f'(x) - a shortcut
- If we know a derivative and a point on the curve f(x), there is a shortcut to solving it
- It's using a command on the CAS called dSolve - for the ClassPad
- Go interactive, advanced, dSolve
- In the first column, type y'=...(derivative)...
- Independent Variable - x
- Dependent Variable - y
- Initial condition, type, for example if we had the point (1, 5) - "x=1,y=5"

Could somebody please give an example as to where to implement this, and what I would input? Can't seem to get it to work.

Same here. Is it possible to do it on the nspire?