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CrossFit415

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Let C: y=8x^5+5x+1 and suppose L is a line through the origin tangent to C at a point P=(a,f(a)) on C.

-Find the coordinates of P

-Compute the slope m sub L of L

Where should I begin? I'm guessing I would need the derivative of the equation f(x)? Then I would use the point slope form to figure out point P?