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Precalculus question. if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h? watch

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    Precalculus question. if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h?
    what brings a and h into all of this?? v confused as i havent done this stuff in a while.
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    (Original post by finewhateverx)
    Precalculus question. if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h?
    what brings a and h into all of this?? v confused as i havent done this stuff in a while.
    This is "differentiation from first principles" which is not simple so I doubt anyone is going to give you a full explanation here.

    I recommend you look in a textbook or search Google for an explanation.
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    (Original post by notnek)
    This is "differentiation from first principles" which is not simple so I doubt anyone is going to give you a full explanation here.

    I recommend you look in a textbook or search Google for an explanation.
    Challenge accepted! :P
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    (Original post by finewhateverx)
    Precalculus question. if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h?
    what brings a and h into all of this?? v confused as i havent done this stuff in a while.
    To find f(a + h) you substitute (a + h) for x into f(x).
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    (Original post by notnek)
    This is "differentiation from first principles" which is not simple so I doubt anyone is going to give you a full explanation here.

    I recommend you look in a textbook or search Google for an explanation.
    thank you i'll look that up
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    (Original post by Muttley79)
    To find f(a + h) you substitute (a + h) for x into f(x).
    sorry but could you explain why?
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    (Original post by notnek)
    This is "differentiation from first principles" which is not simple so I doubt anyone is going to give you a full explanation here.

    I recommend you look in a textbook or search Google for an explanation.
    never mind, they haven't even learnt f(x) notation, you were right
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    (Original post by finewhateverx)
    sorry but could you explain why?
    Have you met function notation?

    For example if f(x) = 5x + 3 then f(2) = (5 x 2) + 3 = 13
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    (Original post by Muttley79)
    Have you met function notation?

    For example if f(x) = 5x + 3 then f(2) = (5 x 2) + 3 = 13
    or, more clearly:

     f(x) = 2x^2 + 4x + 7\

\



f(3) = 2(3)^2+4(3) + 7 = 37\

f(5) = 2(5)^2+4(5) + 7 = 77\
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    (Original post by Callum Scott)
    or, more clearly:

     f(x) = 2x^2 + 4x + 7\

\



f(3) = 2(3)^2+4(3) + 7 = 37\

f(5) = 2(5)^2+4(5) + 7 = 77\
    That's NOT clearer - the function the OP is dealing with is linear - you've just over-complicated it!
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    (Original post by Muttley79)
    That's NOT clearer - the function the OP is dealing with is linear - you've just over-complicated it!
    the function is more complicated, but the idea it conveys is much clearer with more terms, and the LaTex format.
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    (Original post by Muttley79)
    Have you met function notation?

    For example if f(x) = 5x + 3 then f(2) = (5 x 2) + 3 = 13
    yes i am aware of that but
    how can i conclude from the question that i have to substitute (a+h) for x?
    if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h?
    i don't see what brings a and h into all this. sorry it's probably really simple but its been a while and i just can't make anything of it
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    (Original post by Muttley79)
    That's NOT clearer - the function the OP is dealing with is linear - you've just over-complicated it!
    If the OP can't deal with quadratic functions then I doubt they'll be able to handle differentiation from first principles
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    (Original post by notnek)
    If the OP can't deal with quadratic functions then I doubt they'll be able to handle differentiation from first principles
    guys id appreciate it if youd stop being so condescending and help out, or else please leave. for background im done with alevels and in my second yr of med school havent done maths for two years, had to do an Aelective precalculus course, came across this question which for some reason or other i cant seem to be able to make head or tail of. if you can clarify things then please do so and if you cant then honestly whats the point of hanging around?
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    (Original post by Callum Scott)
    the function is more complicated, but the idea it conveys is much clearer with more terms, and the LaTex format.
    Don't overcomplicate a simple idea.
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    (Original post by finewhateverx)
    guys id appreciate it if youd stop being so condescending and help out, or else please leave. for background im done with alevels and in my second yr of med school havent done maths for two years, had to do an Aelective precalculus course, came across this question which for some reason or other i cant seem to be able to make head or tail of. if you can clarify things then please do so and if you cant then honestly whats the point of hanging around?
    I am trying to help - I can't help idiots showing off.

    When you have anything in function notation then that means replace x by whatever is in the bracket - that how function notation is defined.
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    (Original post by finewhateverx)
    guys id appreciate it if youd stop being so condescending and help out, or else please leave. for background im done with alevels and in my second yr of med school havent done maths for two years, had to do an Aelective precalculus course, came across this question which for some reason or other i cant seem to be able to make head or tail of. if you can clarify things then please do so and if you cant then honestly whats the point of hanging around?
    That was being condescending to the person he was replying to :awesome:, not you lol :P
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    (Original post by finewhateverx)
    guys id appreciate it if youd stop being so condescending and help out, or else please leave. for background im done with alevels and in my second yr of med school havent done maths for two years, had to do an Aelective precalculus course, came across this question which for some reason or other i cant seem to be able to make head or tail of. if you can clarify things then please do so and if you cant then honestly whats the point of hanging around?
    I can see how my comment seemed like it was directed at you but it wasn't. I was making a point to Muttley79.

    I'd be the last person to put someone down based on their mathematical knowledge.
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    (Original post by finewhateverx)
    yes i am aware of that but
    how can i conclude from the question that i have to substitute (a+h) for x?
    if f(x) = 3x + 7, find [ f (a + h) - f (a) ] / h?
    i don't see what brings a and h into all this. sorry it's probably really simple but its been a while and i just can't make anything of it
    Just substitute a for x if it's confusing you, h just represents the difference between the two x values.

    If you have two points:  (x, f(x)) & (x+h, f(x+h)) then the gradient of the line that joins them is given by:
    \frac{\Delta y}{\Delta x} = \frac{f(x+h) - f(x)}{(x+h) - x} \equiv \frac{f(x+h) - f(x)}{h}
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    (Original post by Muttley79)
    idiots showing off.
    I put something in LaTex form, with more terms so it became easier to understand!! keep your socks on!
 
 
 
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