Question

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

Answer 1

The given curve y is defined as,

y= x 3 −3x+2

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

slope= ( dy dx ) x= x 0

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

slope= ( d( x 3 −3x+2 ) dx ) x=3 = ( 3 x 2 −3 ) x=3 =24