Calculus Grade 12 University

posted by .

Use the second derivative test to find the local minimum and maximum values of each function, wherever possible.

A) f(x) = 16/x + x^2
B) s(t) = t^4 - 8t^3

  • Calculus Grade 12 University -

    A.
    f ' = -16/x^2 + 2x
    f '' = 32/x^2 + 2

    max/min where f'=0 and f''≠0
    f'(2) = 0
    f''(2) > 0, so f is concave up,
    so f(2) = 12 is a minimum

    similarly for (B)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc

    1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)<0 if x<4 f'(4)=0 …
  2. 12th Calculus

    use the derivative of the function y=f(x)to find the points at which f has a local maximum local minimum point of inflection y'=(x-1)^2(x-2)(x-4)
  3. Calculus

    For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) Graph y = f_c(x) for these values of the parameter c: c = -1, 0, 1, 2, 3, 4. What are the similarities and differences among the graphs, and how do the graphs change …
  4. Calculus

    For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) Graph y = f_c(x) for these values of the parameter c: c = -1, 0, 1, 2, 3, 4. What are the similarities and differences among the graphs, and how do the graphs change …
  5. calculus

    find the local maximum and minimum values of f using both the first and second derivative tests. which method do you prefer?
  6. Calculus (pleas help!!!)

    Let f(x)=e^(2x)-kx, for k greater than 0. Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,1/3,1/2,1,2,4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x= ____ Find …
  7. Calculus Please Help

    Let f(x)=e^(2x)-kx, for k greater than 0. Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,1/3,1/2,1,2,4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x= ____ Find …
  8. Calculus Grade 12 University

    Determine the critical numbers and find the absolute maximum and minimum values of the function y = 8x^3 + x^4 for x e [-8,2]
  9. math

    A function is given by, f(x,y) = x^4 - y^2 - 2x^2 + 2y - 7 Using the second derivative test for functions of two variables, classify the points (0,1) and (-1,1) as local maximum, local minimum or inconclusive.
  10. Please check my Calculus

    1. Find all points of inflection: f(x)=1/12x^4-2x^2+15 A. (2, 0) B. (2, 0), (-2, 0) C. (0, 15) D. (2, 25/3), (-2, 25/3) E. none of these I got D. I found the second derivative and equaled it to 0 and solved for x. I plugged the x values …

More Similar Questions