Question

Find a cubic function f(x) = ax^3+bx^2+cx+d whose graph has horizontal tangents at the points (-2, 6) and (2, 0)

Answer 1

how do i even start this?

Answer 2

find derivative of the function. that will give you the slope of the function.
at the two specified points, the slope is 0. this is basically an extream problem (maxima and minima)

Answer 3

wow ty

Answer 4

also, note that the two points lie on the curve. you have four equations and four unknowns

Answer 5

do i sub x=-2 into the derivative while its set to 0?

Answer 6

bit confused once i get the derivative to solve for a,b,c

Answer 7

yup

Answer 8

ive two equatons and 3 unknowns ?

Answer 9

right. but you know that the two points also happen to lie on the curve. so substitute x = -2 and f(x) =6 in the original equation
substitute the other point too
you will get four equations and 4 unknowns

Answer 10

ohhh