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Slope of tangent line 
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#1
Feb2709, 06:30 PM

P: 55

1. The problem statement, all variables and given/known data
find the slope of the tangent line whose g(x)=x^24 at point (1,3) 2. Relevant equations lim f(x+Δχ) F(c)/ (Δχ) 3. The attempt at a solution g(x)= x^24 G(1+Δχ)= (1+Δχ)^24 ==> Δχ^2+2Δχ3 lim (Δχ^2+2Δχ3)  (3)/(Δχ) = 0 but in the book the answer is 2 so what could I've done wrong? 


#2
Feb2709, 07:13 PM

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P: 21,262

Your last expression (which by the way isn't equal to 0), when simplified a bit, is [itex][\Delta x ^2 + 2 \Delta x  3 + 3]/\Delta x[/itex] = [itex](\Delta x ^2 + 2 \Delta x)/\Delta x[/itex] Factor [itex]\Delta x [/itex] from both terms in the numerator, and cancel with the one in the denominator, then take the limit as [itex]\Delta x[/itex] goes to zero. 


#3
Feb2709, 07:13 PM

HW Helper
P: 3,307

the limt looks ok until you jump to 0, you still have a deltaX on the denominator, which would tend towrds infinty while the top will tend towards zero. so at teh moment you limit is undetermined until you clean it up a bit more...
so you need to cancel deltaX as much as possible before taking the limit 


#4
Feb2809, 05:45 AM

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Slope of tangent line



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