Answer
(3,7) and (-1,-1)
Work Step by Step
Let f(x)= y.
Slope of the tangent to the given curve at (x,y) is
$\frac{dy}{dx}$= $3x^{2}-6x+1$
The slope is given to be 10.
So $3x^{2}-6x+1$=10 ( As the slope of the tangent to the curve y= f(x) at the point ($x_{0},y_{0}$) is given by f'($x_{0}$).)
Or $3x^{2}-6x-9=0$
This gives x= 3 or x= -1
Now, y= $x^{3}-3x^{2}+x+4$
So when x=3, y=$ 27-(9\times3)+3+4= 7$
When x= -1, y= -1-3-1+4= -1
Therefore, the required points are (3,7) and (-1,-1)
