Question

Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct.

y = (x2 − 3x + 3)3 at (2, 1)

Step 1

Given a function y =( x^{2} -3x+3)^{3} . We need to find the equation of the tanget line at (2,1).

The slope of the tangent line of a function at x=a is given by f'(a). So here we find the derivative of the given function at point (2,1) to calculate the slope.

Step 2

Differentiating the given function with respect to x and plug in x = 2 we get the slope of the tangent line as 3.

Step 3

We know a point on the line (2,1) and slope of the line as 3.

The equation of line with slope m and passing through point (x1,y1) is given by

(y-y1...

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