anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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DanJS
  • DanJS
you are given 2 points on the function,
anonymous
  • anonymous
ya I realize that
anonymous
  • anonymous
I just don't know how to plug them in to solve since there are several variables

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DanJS
  • DanJS
which class
DanJS
  • DanJS
put in both points, see what you get first in terms of a system of equations in the constants a,c,d
DanJS
  • DanJS
10 = -64a + 16c + d d = 7
DanJS
  • DanJS
is this calc class, or before derivatives
DanJS
  • DanJS
because you have 2 variables but one equation, they give you max and min points though, the derivative is 0 at those
anonymous
  • anonymous
I'm still kind of lost
DanJS
  • DanJS
use the two points given (x , f(x)) and you get an equation for each one 10 = -64a + 16c + d 7 = d
DanJS
  • DanJS
overall, you have one equation and 2 variables left, cant solve , need another relationship with a and b ,
DanJS
  • DanJS
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
DanJS
  • DanJS
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
DanJS
  • DanJS
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
DanJS
  • DanJS
a and c , sorry
DanJS
  • DanJS
i got a=3/32 and c=9/16, and d =7 from before
DanJS
  • DanJS
you follow all that?
anonymous
  • anonymous
thanks!

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