Question

Find a cubic function f(x)=ax^3+cx^2+d that has a local maximum value of 10 at -4 and a local minimum value of 7 at 0

Answer 1

you are given 2 points on the function,

Answer 2

ya I realize that

Answer 3

I just don't know how to plug them in to solve since there are several variables

Answer 4

which class

Answer 5

put in both points, see what you get first in terms of a system of equations in the constants a,c,d

Answer 6

10 = -64a + 16c + d

d = 7

Answer 7

is this calc class, or before derivatives

Answer 8

because you have 2 variables but one equation, they give you max and min points though, the derivative is 0 at those

Answer 9

I'm still kind of lost

Answer 10

use the two points given (x , f(x)) and you get an equation for each one

10 = -64a + 16c + d

7 = d

Answer 11

overall, you have one equation and 2 variables left, cant solve , need another relationship with a and b ,

Answer 12

the derivative is

f ' (x ) = 3a*x^2 + 2c*x

Using this because they tell you those points are max/min locations, here f ' (x) = 0

Answer 13

So at the point (-4 , 10) there is a horizontal tangent line, the first derivative is zero, it is a maximum value

you can use x=-4, and f ' (x)=0, that will give you another relationship between 'a' and 'b', might be able to get a solution now

Answer 14

the two equations you have now are

10 = -64a + 16c + 7 ---(d=7)
and
0 = 48a - 8c

may get values for 'a' and 'b' after solving those

Answer 15

a and c , sorry

Answer 16

i got a=3/32 and c=9/16, and d =7 from before

Answer 17

you follow all that?

Answer 18

thanks!