The curve y = x 3 + ax 2 + b has a stationary point at (4,

Question:

The curve y = x3 + ax2 + b has a stationary point at (4, −27).

a. Find the value of a and the value of b.

b. Determine the nature of the stationary point (4, −27).

c. Find the coordinates of the other stationary point on the curve and determine the nature of this stationary point.
d. Find the coordinates of the point on the curve where the gradient is minimum and state the value of the minimum gradient.

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