a. Given that f(x) = x 3 3x 2 + 4x + 1, find f(x). b.

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a. Given that f(x) = x3 − 3x2 + 4x + 1, find f´(x).

b. The point P is on the curve y = f(x) and its x-coordinate is 2.

i. Calculate the y-coordinate of P.

ii. Find the equation of the tangent at P.

iii. Find the equation of the normal at P.

c. Find the values of x for which the curve has a gradient of 13.

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