(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The curve C has equation [tex] y=k x^3-x^2+x-5 [/tex] where k is a constant.

A) Find the derivative of the function with respect to x

The point A with x-coordinate [tex] -\frac{1}{2} [/tex] lies on C. The tangent to C at A is parallel to the line with equation [tex] 2 y-7 x+1=0 [/tex] .

Find...

B) the value of k

C) the value of the y-coordinate at A.

2. Relevant equations

C is [tex] y=k x^3-x^2+x-5 [/tex]

Equation of the line parallel to the tangent of C at A ( [tex] -\frac{1}{2} [/tex]) [tex] 2 y-7 x+1=0 [/tex] .

3. The attempt at a solution

Ok, so I have found the derivative to be equal to: [tex] y'=3 k x^2-2 x+1 [/tex]

I am having trouble with the find y (and k) because if you were to solve that equation by substituting into it x we then have: [tex] \frac{1}{2} (7 x-1)=y=-2.25 [/tex] but that y value isn't on the tangent line to C. So how would i go about completing these problems?

Thanks

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Differentiation Question help

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