Calculus: Determine the constants from function

The function h(x) = x^3 + bx^2 + d has a critical point at (2, -4). Determine the constants b and d and find the equation of h(x).

IM SO CONFUSED :(

asked by mia
  1. dh/dx = 0 at critical points

    dh/dx = 3 x^2 + 2 b x = 0
    x (3x+2b) = 0
    so
    at (2,4), 3x+2b = 0 = 6 + 2b
    so b = -3
    so
    h = x^3 -3 x^2 + d
    at x = 2, h = -4
    -4 = 8 - 12 + d
    d = 0
    so
    h = x^3 -3 x^2

    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    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
  2. Critical Points

    find values for a, b, and c so that the function f(x) = x^3 + ax^2 + bx+ c has a critical point at (1,5) and an inflection point at (2,3). I got a as -6, but I don't know what b and c are. For b and c I just have b + c= 10. I do
  3. Critical Points, Etc.

    find the values for a, b, and c such that the function f(x)= x^3 + ax^2 + bx+ c has a critical point at (1,5) and an inflection point at (2,3). a= -6 b= 3 c= 7 i got those, but they're wrong. i'm not sure why. :/
  4. 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?
  5. Diff Calculus

    Find the interval(s) where the function is increasing of decreasing. find the: a) critical value(s) b) critical point(s) c) max. value + max. point d) min.value and min. point e)point on inflection if there is: 1)
  6. Calculus

    Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a
  7. CAL-Critical points

    For the function F(x) = inx/x^2 , find the approximate location of the critical point in the interval (0, 5).
  8. calculus

    Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function f(x,y)= 3x^2 - 3e^5y^2
  9. calculus

    Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function. f(x,y)=3x^2 - 3xy + 3y^2 +5
  10. Calculus

    Please check, if there is something wrong please explain what I did wrong. Thank you! Calculate the d^2y/dx^2. y= e^-x + e^x y' = e^x - e^-x y'' = e^x + e^-x Find the x-coordinace of all critical points of the given function.
  11. Please check my Calculus

    1. Which of the following describes the behavior of f(x)=x^3-x A. Relative maximum: x=0 B. Relative maximum: x=(1/sqrt(3)); Relative minimum: x=(-1/sqrt(3)) C. Relative maximum: x=(-1/sqrt(3)); Relative minimum: x=(1/sqrt(3)) D.

More Similar Questions