Find the points on the graph that have tangent lines with the given slope.
f(x) = 16/x-6, m=-4
No matter what I try, I can't find the correct answer.
I guess it's my algebra..
I know that you have {(16/x-6) - (16/c-6) } all divided by x-c..
its just the algebra that follows this that I'm making a mistake. Help! Please!
f(x) = 16/x-6, m=-4
No matter what I try, I can't find the correct answer.
I guess it's my algebra..
I know that you have {(16/x-6) - (16/c-6) } all divided by x-c..
its just the algebra that follows this that I'm making a mistake. Help! Please!
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Okay, so you need to compute the limit. Let me simplify the expression first and then take the limit.
[16/(x - 6) - 16/(c - 6)]/(x - c) = [16(c - 6) - 16(x - 6)]/[(x - 6)(c - 6)(x - c)] =
=16(c - x)/[(x - 6)(c - 6)(x - c)] = -16/[(x - 6)(c - 6)].
Note that to get the last term on the right, I used the fact that (c - x) in the numerator cancels with (x - c) in the denominator but leaves the factor -1. Okay, now take the limit as x-> c.
f ' (c) = lim -16/[(x - 6)(c - 6)] = -16/(c - 6)².
. . . . . x->c
You are interested in finding those value(s) of c for which this is equal to -4. This gives a simple equation for c.
-16/(c - 6)² = - 4 ==> 4 = (c - 6)² ==> c - 6 = ± 2.
There are two values c = 8 and c = 4.
[16/(x - 6) - 16/(c - 6)]/(x - c) = [16(c - 6) - 16(x - 6)]/[(x - 6)(c - 6)(x - c)] =
=16(c - x)/[(x - 6)(c - 6)(x - c)] = -16/[(x - 6)(c - 6)].
Note that to get the last term on the right, I used the fact that (c - x) in the numerator cancels with (x - c) in the denominator but leaves the factor -1. Okay, now take the limit as x-> c.
f ' (c) = lim -16/[(x - 6)(c - 6)] = -16/(c - 6)².
. . . . . x->c
You are interested in finding those value(s) of c for which this is equal to -4. This gives a simple equation for c.
-16/(c - 6)² = - 4 ==> 4 = (c - 6)² ==> c - 6 = ± 2.
There are two values c = 8 and c = 4.