Selam N. answered • 06/26/15
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Mathematics Teacher
m = dy/dx
dy/dx = 3x2 - 3
The eqn of the tangent line to the graph of the function is 3x2 - 3.
The eqn of the slope of the tangent line to the graph of the given function at x= 2 is, therefore,
step 1: 3(2)2 - 3= 9.
point of tangency,
x=2, y=(2)3 - 3(2) + 4
(2,6)
Step 2: y=mx + b,
6 = 9(2) + b
b= -12
y=9x -12
Dion S.
Okay that makes sense.
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06/26/15
Dion S.
Im sorry one more question where did you get the 9 from in 6 = 9(2) + b the 6 makes sense 3(2) = 6 right but where did you get the 9.
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06/26/15
Selam N.
m, the slope is equal to dy/dx at any point x. However, to evaluate m when x=2, plug in 2 for x, 3(2)2 - 3=9. The slope, m=9 at x=2.
using the slope-intercept form of the eqn of a line, y=mx + b, where m=9, at the point of tangency, (2,6), solve for b, the y-intercept.
6=9(2) +b.
b =-12
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06/26/15
Dion S.
Find the derivative of each function.
y = 1/x-1
y = 1/x-1
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06/28/15
Selam N.
dy/dx = d(x-1)/dx -d(1)/dx
= -(x)-2
=-(1/x2 )
However, if your question is, y = 1/(x-1)
dy/dx = [ d(1)/dx • (x-1) - (1)d(x-1)/dx]/(x-1)2
Use the Quotient Rule
=[0 -(1)]/(x-1)2
=-1/(x-1)2
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06/28/15
Dion S.
06/26/15