A cubic polynomial function f is defined by:
f(x)=4x^3+ax^2+bx+k
where a, b, and k are constants. The function f has a local minimum at x=-1, and the graph of f has a point of inflection at x=-2.
1) Find the values of a and b
2) If the integral from 0 to 1 of f(x)dx = 32, what is the value of k?
1. f(x)=4x^3+ax^2+bx+k
2. Therefore, f’(x)=12x^2+2ax+b, f”(x)=24x+2a
3. Solve: f’(-1)=12-2a+b=0, f”(-2)=-48+2a=0
4. Obtaining: a=24, b=36
5. The integral from 0 to 1 of f(x)dx = 32 -> 27+k=32 -> k=5
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no one in the world would understand what you mean
only if they already understood what a polynomial, inflections, constants, intergral, local minimum, your varialbles what they mean, what you mean and how they work in the real world.
if you were writing an essay on calculus and used this you’d get zero marks.
in english you have to make sense.
I don’t understand where you are getting the 27 from in answer number 5?
The both of you are really arrogant. Thanks, we’re all completely disgusted, annoyed, and unimpressed (especially since Erica apparently can’t use proper grammar). But as someone that wants to leave a real message, thanks for the help Elliot. Your explanation was really clear and easy to understand!
I did this so easy.
I guess being in grade 8 and doing Calc. really paid off.
That was fun!
Wow…I remember how to do that and it’s been 3 years since I’ve really worked with that sort of Calc.
Fun, fun, fun.