Calculus

posted by .

How many critical points does the function

f(x) = [(x-2)^5][(x+3)^4] have?

A. 1
B. 2
C. 3
D. 5
E. 9

---

Ok, these are my thoughts on this question:
My impulse was to do derivative of the function. However, if I'm going to set the function equal to zero to find some critical points (because a critical point is where derivative either equals zero or doesn't exist), it's going to take me forever, and this question shouldn't take very long.

So my next choice was to look at the function itself. The degrees are 5 and 4, so if we add those degrees together we get 9. Essentially, I thought the answer would be E because of 9 factors, 9 CPs. However, the factors repeat, 2 and -3!

Thus, my guess is B, which is two. Are my reasonings right?

Thanks much!

  • Calculus -

    Your first impulse was correct and made sense, but then you slipped into some very fuzzy thinking.
    How can you just add the exponents when the bases are not the same??

    So from your impulse ....

    f'(x)= (x-2)^5(4)(x+3)^3 + (x+3)^4(5)(x-2)^4
    =(x-2)^4 (x+3)^3 [ 4(x-2) + 5(x+3)]
    = (x-2)^4 (x+3)^3 (9x +7)

    x=2, x=-3 , and x = -7/9 will produce critical points.

    What was so hard about that?

  • Calculus -

    oh god. didn't even think about factoring. lol thanks

  • Calculus -

    lol rice krispies am i right

  • Calculus -

    But you did it wrong

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. URGENT! Last calculus question!

    Hey! So, I was wondering if someone could answer this. I am mad studying for my exam and I still have a few questions left that I just don't have time to answer, and the assignment is due tomorrow. Thanks and here is the question: …
  2. calculus

    How many critical points does the function: (x+2)^5 * (x-3)^4 have?
  3. calculus

    Use a graph of f(x) = 3 e^{-8 x^2} to estimate the x-values of any critical points and inflection points of f(x). critical points x= Inflection points x= Next, use derivatives to find the x-values of any critical points and inflection …
  4. Please help with Physics Quickly

    1. How are impulse and momentum related? (Points : 1) Impulse is the change in momentum of an object. Momentum is the change in impulse acting on an object. Impulse and momentum are always equal in magnitude. Impulse and momentum are
  5. Calculus

    Sketch the graph of the function that has the following properties. f is continuous on (-infinity, infinity). points: (-1,2), (0, 0), (-1,0) f'(x)>0 at (-infinity, -1) f'(-1)=0 f'(x)<0 at (-1, 1) f'(1)=0 f'(x)>0 on (1, infinity) …
  6. Calculus

    A continous function y=f(x) crosses x-axis at points x=-3,0,2,5. Use mean value theorem to show that function has three critical points?
  7. Calculus

    How many critical points does the function f(x) = e^x - x^3 have?
  8. calculus

    One litre of water at 0 degrees Celsius will have a different volume at higher temperatures. For a temperature 0 ≤ T ≤ 30 (in Celsius) this volume (in litres) is well approximated by the function V = −aT 3 + bT 2 − cT + 1 using …
  9. Math - extreme values

    Identify the critical points and find the extreme values on the interval [-1,-5) for f(x)=cosx+xsinx+3 I've taken the derivative which gives me f'(x)=xcos(x). I know I have to solve to get the critical points and then plug in the critical …
  10. Math - Calculus

    Are endpoints also critical points? I'm trying to find the critical points of a function on the interval [-1,5]. So far,the only critical point I have is 2. Does that mean -1 and 5 are also critical points?

More Similar Questions