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

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    (Original post by Callum Scott)
    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}
    Callum you really aren't helping at the moment ...
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    (Original post by Muttley79)
    Callum you really aren't helping at the moment ...
    Let him be the judge of that... Don't be condescending now.
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    (Original post by Callum Scott)
    I put something in LaTex form, with more terms so it became easier to understand!! keep your socks on!
    It wasn't helping making an expression quadratic and 'showing off' by using LaTex when it just wasn't needed.
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    (Original post by Callum Scott)
    Let him be the judge of that... Don't be condescending now.
    You are answering a question the OP isn't asking.
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    (Original post by Callum Scott)
    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}
    i get the second part of what you say of course but i still cannot see how the thing can be solved by substituting..thanks all for your help but i think ill just ask my teacher..and take this as a lesson to be less timid and speak up in class..thanks
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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
    f(a + h) means substitute x = a + h into f

    a and h are used by convention in differentiation from first principles. a is any specific value of x and h is a small number.
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    PS Reviewer
    Guys, please stay on topic and help the OP here. Thank you
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    (Original post by finewhateverx)
    i get the second part of what you say of course but i still cannot see how the thing can be solved by substituting..thanks all for your help but i think ill just ask my teacher..and take this as a lesson to be less timid and speak up in class..thanks
    Substituting works because you have x in the expression you have been given but the calculation you are asked to perform contains f(a+h) and f(a) so you must work out work f(x) is by substituting a+h and then a and calculating f(a+h) and f(a).

    f(x)=3x+7 if the question was what was f(a^2) then you would have to substitute x=a^2 f(a^2)=3(a^2)+7=3a^2+7, you need to substitute because the question involves different variables than the expression you have been given.
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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.
    \frac {f(a+h)-f(a)} {h}=\frac{(3(a+h)+7)-(3a+7)}{h}=\frac{3a+3h+7-3a-7}{h}=\frac{3h}{h}=3

    Note that if f(x)=3x+7, then f(a+h)=3(a+h)+7=3a+3h+7

    Think of the x in f(x) as just a placeholder.
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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
    (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
    OP function notation is this:
    Spoiler:
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    (Original post by Muttley79)
    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)
    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
    If you've got a function written as f(x), f(STUFF) means "substitute (STUFF) for x everywhere in f".
 
 
 
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