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Leni [432]
3 years ago
13

Find a cubic function y = ax³ + bx² + cx + d whose graph has horizontal tangents at the points (-2,12) and (2,6).

Mathematics
1 answer:
natima [27]3 years ago
6 0
<span>You have four unknowns: a, b, c and d and therefore you will need 4 equations to solve for them. 
</span>You are already given two points ON the curve: (-2, 12) and (2,6). Plug the numbers into the function and you have two equations. Then, ...
<span>To find the slope, take the derivative of the function. "Horizontal tangent" means the slope at those points are zero.
</span><span>Plug the x values of -2 and 2 and set the corresponding y' to zero and you will have two more equations. Solve the 4 simultaneous equations to find a, b, c and d.</span>
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