Question

Let f(x0=x^3+Ax^2+Bx-15 be a function whose graph has a maximum at x=2 and a point of inflection at x=3. Find the values of A and B?

Answer 1

What is f'(x)?

Answer 2

\[f(x)=x^3+Ax^2+Bx-15\]

Answer 3

sorry i miss read that.

Answer 4

Now find f'(x).

Answer 5

f'(x)=\[3x^2+2Ax+B\]

Answer 6

and then f''(x)

Answer 7

\[f"(x)=6x+2A\]

Answer 8

OKay so how do we find the maxima of a polynomial?

Answer 9

Am I suppose to plug something in?

Answer 10

yes that's right :)

Answer 11

So I plug the two into the original function right? Then plug the 3 into the second derivative?

Answer 12

Do you know what is inflection point and critical points?

Answer 13

Critical values are the zeros of the 1st dervivative and inflection points are the zeros of the 2nd derivative?

Answer 14

Yes for the first but for the second that is only necessary condition but not sufficient condition.

Answer 15

One also needs the lowest-order non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection.

Answer 16

So what do I need to do? I'm confused now

Answer 17

If I haven't made any error then \( A=-9 \) and you can find B accordingly :)

Answer 18

Ignore my second last comment if it confuses you. Plug in x=3 in f''(x)=0 and then x=2 in f'(x)=0

Answer 19

aha! I understand thanks!! :)

Answer 20

Glad to help :)

Answer 21

okay last one please?

Answer 22

New thread.

Answer 23

\[Let f(x)=5^1/3+x^2.For what values of x does the instantaneous rate of chnage equal when the rate of change is 3.119?\]