Calculus: Determine the constants from function
posted by mia .
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 :(

Calculus: Determine the constants from function 
Damon
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
Respond to this Question
Similar Questions

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 
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 
Calculus
The population (in thousands) of the Tzitzit bird is well described by a function of the form P(t) = ae^kt, where t is the time in years and a and k are constants. If the population was 10 thousand when t0 and 300 thousand when t=3, … 
math
express y=0.1(1000)^x in the form lg y =mx+c ,where m and c are constants ,and x is a function of x . Determine the constants m and c and the function x . 
Calculus
The function h(x) = x^3+bx+d has a critical point at (2,4). Determine the constants b and d and find the equation of h(x). Show your work. 
Calculus
The function h(x) = x^3+bx+d has a critical point at (2,4). Determine the constants b and d and find the equation of h(x). I'm very confused and I do not have any idea on what the first step is. 
Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4x)x^3 for x>0. A. Find the xcoordinate of the critical point of f. Determine whether the point is a relative … 
Maths
Given the equation y=2x4 of an exponential function f 1)write down the equation of horizontal asymptote of f 2)determine the y intercept of f 3)determine the y value of a point on f with x=2 4)draw the graph of the function of f … 
calculus
find the constants a and b so the function is continuous on a real line piecewise function: f(x)={5, if x<= 2; ax+b, if 2<x<3; 5, if x>=3 I know the limit x>2 is 5 and limit x>3+ is 5. I don't know how to … 
PreCalc 12
Let f(x)=a(xp)^2+q be a quadratic function, where a,p,q are constants and a≠0. f(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define g(x) be the function after …