Question

How many tangents are possible from the origin on the curve y=(x+1)^3 . Also find the equation of these tangents . HELP !

Answer 1

this a calculus course?

Answer 2

Yes , its a question from application of derivatives.

Answer 3

a point on the curve looks like \((x, (x+1)^3)\) and the origin is \((0,0)\)
the slope of the line between \((0,0)\) and \((x,(x+1)^3)\) is \(\frac{(x+1)^3}{x}\)

Answer 4

the slope of the line tangent to the graph will be \(3(x+1)^2\)

Answer 5

that being the derivative
they have to be the same, set
\[3(x+1)^2=\frac{(x+1)^3}{x}\] and solve for \(x\)

Answer 6

Thanks a ton :)

Answer 7

yw, hope it is clear more or less

Answer 8

Yep , my answer matches :)