Saturday

October 10, 2015
Posted by **Bob** on Friday, June 28, 2013 at 4:03pm.

- Calculus (help steve) -
**Steve**, Friday, June 28, 2013 at 4:20pmf(x) = −8x^3+6ax^2−3bx+4

f'(x) = -24x^2 + 12ax - 3b

Now, local extrema occur where f'(x) = 0.

Since we see that f(x) is quadratic, and we know two zeros, we know that those are the only two zeros.

So, we know that

f'(x) = k(x-1)(x-3)

= kx^2 - 4kx + 3k

Take the antiderivative to see that

f(x) = k/3 x^3 - 2kx^2 + 3kx + C

Equating coefficients with the given f(x), we have

k/3 = -8, so k = -24

-2k = 48 = 6a, so a = 8

3k = -72 = -3b, so b = 24

a+b = 32

Check:

f(x) = -8x^3 + 48x^2 - 72x + 4

f'(x) = -24x^2 + 96x - 72

= -24(x^2 - 4x + 3)

= -24(x-1)(x-3)

- Calculus (help steve) -
**Bob**, Friday, June 28, 2013 at 5:35pmThanks Steve.

But apparently, that's not the right answer, since a and b are not local minimum and maximum values.

- Calculus (help steve) -
**Steve**, Friday, June 28, 2013 at 6:12pmGot me. f(x) has a and b as coefficients.

Don't see how they can also be the local min and max.

Maybe you can figure out what they're asking.

Hmmm.

f(x) = −8x^3+6ax^2−3bx+4

f(1) = -8+6a-3b+4 = -4+6a-3b

f(3) = -216+54a-9b+4 = -212+54a-9b

So, if a and b are min and max, then

-4+6a-3b=a

-212+54a-9b=b

or

5a-3b = 4

54a-10b = 212

a = 149/28

b = 211/28

a+b = 90/7

Check:

f(x) = -8x^3 + 447/14 x^2 - 633/28 x + 4

f(1) = 149/28

f(3) = 211/28

If that's not right, I'm stumped what they want.

- Calculus (help steve) -
**Bob**, Friday, June 28, 2013 at 9:12pmIt's not right either. I know, I'm stumped too.

- Calculus (help steve) -
**Bob**, Friday, June 28, 2013 at 9:12pmBut thanks for all the help.

- Calculus (help steve) -
**Ray**, Friday, June 28, 2013 at 9:29pmi had trouble with this problem too

- Calculus (help steve) -
**Steve**, Saturday, June 29, 2013 at 4:03pmCould it be that the coefficients a and b are not the min and max a and b?

If f(x) = -8x^3 + 48x^2 - 72x + 4

Then f(1) = -28 and f(3) = 4

In that case, min+max (or, a+b) = -24

- Calculus (help steve) -
**Steve**, Saturday, June 29, 2013 at 10:57pmOops. |a+b| = 24