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Question

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

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Solution

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


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