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It is known that the equation of tangent of curve C, y = x ^ 3 + AX-8 at x = 2 is y = 15x + B (1) Finding the value of real numbers a and B (2) If the tangent l of curve C passes through point P (4 / 3, - 4), the equation of line L is obtained
【1】 The function y = x & sup3; + AX-8. The derivation is: y '= 3x & sup2; + A. from the problem, we can see that when x = 2, the function y = 2A. The derivative y' = 12 + a = 15. = = = > A = 3. The tangent equation is y-2a = 15 (X-2). = = = > y = 15x-24. That is, a = 3, B = - 24. [2] the function y = x & sup3; + 3x-8. Y '= 3x & sup2; + 3
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