At how many points on the curve y=4x^5-3x^4+15x^2+6 will the line tangent to the curve pass through the origin.
The only way I know how to go about this problem is to find the derivative and thats it. Please Help!
It depends on how many different roots the equation has.
Observe that between any 2 different roots that attains a maximum/minimum in the interval .
And there exists a with where the tangent at passes through the origin.
But we might just as well calculate how many maxima/minima f(x) attains:
Thus if you find all different "real " roots of you're done.
Edit: You don't even have to find the roots of explicitly. You can use the intermediate value theorem to decide how many roots in this equation has.