SOLUTION: The graph of y = 2x^3 + ax^2 + b has a stationary point (-3,19) . Find the value of a and b. Determine the nature of the stationary point (-3,19).

Question 1192428: The graph of y = 2x^3 + ax^2 + b has a stationary point (-3,19) . Find the value of a and b. Determine the nature of the stationary point (-3,19).
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The stationary point at x=-3 is where the derivative is zero.

Use that value of a to solve for b.

The function is

We know f(-3)=19; and f(0)=-8. Those two points, along with the positive leading coefficient, tell us that the stationary point at (-3,19) is a local maximum.

Or, more formally, to show that the stationary point is a local maximum, we could find the second derivative of the function and show that it is negative at x=-3.

ANSWERS:
a=9
b=-8
(-3,19) is a local maximum

A graph....

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