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Question
Find the equation of the tangent line to the graph of f(x)=x^2/3 that is parallel to the line y=4x-3. Express your answer in slope-intercept form.
I know that the derivative is 2x/3 but I don't know how to plug it into the slope-intercept form to get the answer.
That's right, the slope of the tangent line is m=2x/3 . we need to know x in order to get the
slope as a value . Note that this tangent line is parallel to the line y=4x-3 ... that menas
that the multiply of the two slopes is -1 , thus : (2x/3)*4=-1 --> x=-3/8 . therefore m=-0.25
Now, we know that the tangent line passes throught the point ( -3/8,f(-3/8) ). Hence,
6/64=(-1/4)(-3/8)+n --> n=0 .
The equation of the tangent line will be : y=-x/4
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Answers by Expert:
Alon Mandes
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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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