posted by .

Find the values for which f(x) = x^10-10x and if 0 (less than or equal) to x (which is less than or equal to) 2.

a) f(x)has a local max or local min. Indicate which ones are max and which are mins.

b) f(x) has a global max or global min

could you kind of give me a hint on how to start and solve this question? i'm not really sure how to start working on it.

  • Calculus -

    0 </= x </= 2 is the domain?
    y = x^10 - 10 x
    if you graph this it will start at 0, drop below axis, come back up to 0 when x^9 = 10 (about x = 1.3) and take off like mad up to the right
    so part a
    dy/dx = 10 x^9 - 10
    zero when x^9 = 1
    or when x = 1
    that is in our domain and we already know it is a min but to prove it find y"
    y" = 90 x^8 where x = 1
    so y" is positive so this is a minimum at x = 1
    y = 1^10 - 10 = -9
    (1, -9) is local min
    local max will be where x = 2 if y>0 there
    y = 2^10 - 20
    y = 1024 - 20 = 1004
    (2, 1004) is the maximum in the domain

    outside our domain x^10 is even so goes to oo for negative x and the -10x term is positive for negative x so it never drops below zero to the left of the origin and has no minima before heading off to +infinity for large -x

  • Calculus -

    thank you so much, that makes so much more sense now!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find the cubic function f(x)=ax^3+bx^2+cx+d that has a local max value of 3 at -2 and a local min values of 0 at 1. I have no idea how to solve this. Could you please give step by step answers and explanations for the steps. Thanks!
  2. calculus

    I don't understand how to do this? I don't know the steps on how to do it! Can you please just tell me the steps?
  3. Math

    find any stationary points of the function g(x) = (2x-3)square root of 5+16x-4x^2 (0 less than or equal to x less than or equal to 4) and use the first derivative test to classify each stationary point as a local maximum or local minimum …
  4. Calculus

    Find any absolute max/min and local max/min for the function f(x)=x^3-4x+5 on the interval [0,5). Made sure to prove that these points are max/min values. This is what I did so far. f'(x)=3x^2-4=0 3x^2=4 x= 2/sqrt3 The -2/sqrt3 is …
  5. Calculus - You wont get it

    Find the local max and local min and saddle points of f(x, y) = x^4 + y^4 - 4xy +1
  6. calculus

    find max and min of e^x-e^(3x) on interval where x is greater than or equal to 0 and less than or equal to 1
  7. calculus

    Sketch the curve y = x^3 - 12x^2 + 36x I already did the question properly it is concave down at (0,4) and concave up at (4,infinity) I found the abs max to be (2,32) and abs min to be (6,0) What I wanted to know is when labeling the …
  8. Cal/Math

    F(x) = 3-2x, x is less than or equal to 5 F(x)= e^x find the absolute and local max and mins of f
  9. calculus

    Find the correct values for the equation -x^3 +bx^2 +cx + d, using this information, local min x= -5, local max (1,11). Point of inflection = -2.
  10. math

    Find the value(s) of x for the following. (Enter your answers as a comma-separated list.) f(x) = 6 sin^2 x − 6 cos x, and the interval is 0 is less than or equal to x and x is less than or equal to pi. (a) f(x) has a local maximum …

More Similar Questions