Question

Find the slope of the tangent to curve y = x 3 − x + 1 at the point whose x -coordinate is 2.

Answer 1

The given curve y is defined as,

y= x 3 −x+1

Slope of tangent to a curve y at a given point x= x 0 is given by,

slope= ( dy dx ) x= x 0

The point whose x coordinate is given as x=2.

Substitute x 3 −x+1 for y and 2 for x 0 .

slope= ( d( x 3 −x+1 ) dx ) x=2 = ( 3 x 2 −1 ) x=2 =11