The curves (y=4 x^2+2 x-8 ) and (y=x^3-x+13 ) touch each other at the point

Step-by-step solution

(y=4 x^2+2 x-8 ) differentiate w.r.t. ' (x ) ' on both sides, ( aligned d y d x & =4(2 x)+2(1) d y d x & =8 x+2 (i) y & =x^3-x+13 aligned ) differentiate w.r.t. ' (x ) ' on both sides, ( d y d x =3 x^2-1 (ii) ) Since, curves are touch each other ( aligned & & 8 x+2 & =3 x^2-1 & & 3 x^2-8 x-3 & =0 & & (x-3)(3 x+1) & =0 & & x & =3 (or) -1 3 aligned ) Put, (x=3 ) in (y=x^3-x+13 ) ( aligned & y=3^3-3+13 & y=37 aligned ) ( ) Point of contact (P=(3,37) )