Question 163395
given: f(x)=5x-x^2
find: f(5-h)-f(5)/h
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f(x) = 5*x - x^2
f(5-h) is gotten by replacing x with (5-h), so
{{{f(5-h) = 5*(5-h) - (5-h)^2}}}
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f(5) is gotten by replacing x with 5, so
{{{f(5) = 5*5 - (5)^2}}}
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since there is no parentheses around it, your formula f(5-h)-f(5)/h
is assumed to be:
{{{f(5-h) - (f(5)/h)}}}
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if you meant {{{(f(5-h) - f(5))/h}}}, that would be a different equation.
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i'll solve for
{{{f(5-h) - (f(5)/h)}}}
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{{{f(5-h) - (f(5)/h) = 5*(5-h) - (5-h)^2 - ((5*5 - (5)^2)/h)}}}
this becomes
{{{25 - 5*h - (25-10*h + h^2) - ((25-25)/h)}}}
which becomes
{{{25 - 5*h - 25 + 10*h - h^2 - (0/h)}}}
which becomes
{{{5*h - h^2}}}
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as far as i can tell.
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if you really meant {{{(f(5-h) - f(5))/h}}}, then the equation becomes
{{{(5*(5-h) - (5-h)^2 - (5*5 - (5)^2))/h}}}
which becomes
{{{(25 - 5*h - 25 + 10*h - h^2 - 25 + 25)/h}}}
which becomes
{{{(5*h - h^2) / h}}}
which becomes
{{{5 - h}}}
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either way the key is to substitute (5-h) for x in f(5-h), and to substitute (5) for x in f(5)
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