Saved Bookmarks
| 1. |
The curves `y=4x^(2)+2x-8` and `y=x^(3)-x+13` touch each other at the point |
|
Answer» The curves `y=4x^(2)+2x-8` and `y=x^(3)-x+13` touch each other at the pont `(3,34)` Give, equation of curves are `y=4x^(2)+2x-8` and `y=x^(3)-x+13` `therefore (dy)/(dx)=8x+2` ltbgt and `(dy)/(dx)=3x^(2)-1` So, the slope of both curves should be same `therefore 3x^(2)-9x+x-3=0` `rArr 3x(x-3)+1(x-3)=0` `rArr (3x+1)(x-3)=0` `therefore x=-1/3` and x=3. For x`=-1/3`, `y=4.(-1/3)^(2)+2.(-1/3)-8` `=4/9-2/3-8=(4-6-72)/(9)` `=-74/9` and for x=3, y=`4.(3)^(2)+2.(3)-8= 36+6-8=34` So, the required points are `(3,34)` and `(-1/3, -79/9)`. |
|