Find the possible values of c for which the line 24x+3y+c=0 is tangent to the curve f(x)=1/3x^3+9/x

Original post by cool11111111111

Find the possible values of c for which the line 24x+3y+c=0 is tangent to the curve f(x)=1/3x^3+9/x

(edited 1 month ago)

tried finding the gradient of the tangent, but I'm not sure really how to approach the question, or what method to use

Original post by cool11111111111

tried finding the gradient of the tangent, but I'm not sure really how to approach the question, or what method to use

Original post by mqb2766

A tangent has the same value and derivative (at a point) as a function. So you have to find the points where the line is a tangent to the function and then find the y intercept c. A bit of looking ahead / sketch should get you thinking about where the line has the same gradient as the function, then think about how the values match.

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