calculus

posted by .

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

  • calculus -

    Start with defining the function:
    f(x)=ax²+bx+c
    Find its derivative:
    f'(x)=2ax+b
    1. f'(1)=8 =>
    2a(1)+b = 8 ....(1)
    2. f'(-2)=-4 =>
    2a(-2)+b = -4 ...(2)
    Solve system of equations (1) and (2) for a and b. (a=2,b=4)

    The parabola is tangent to the line y=-8 => y=-8 is the minimum.

    Now find the minimum of f(x) by setting f'(x)=0 and solve for x.
    f'(x)=2ax+b=0
    2(2)x+(4)=0
    x=-1
    So
    f(-1)=-8
    2(-1)²+4(-1)+c = -8
    so c=-6
    =>
    f(x) = 2x²+4x-6

    Do some checking to make sure the function satisfies all the conditions (and in case I make an arithmetic error):
    given conditions to be checked:
    f(1)=8
    f(-2)=-4
    minimum f(x)=-8

  • calculus -

    find the slope of the tangent line to the graph of e^xy=x at (1,0)

    write an equation of the tangent line

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    55. Find an equation of the tangent line to the graph of f(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x) - (3/2) b) No solution c) No solution For each function, find the points on …
  2. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 7 x - 2 x^2 text( at ) \(-1,-9\) m = y =
  3. Calculus PLEASE HELP

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2 x - 4 x^2( at ) (-2,-20) m= y=
  4. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph …
  5. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4)
  6. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y =
  7. Calculus

    Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = -8/5 x^2 + 7 x + 7;(-1, -8/5) slope tangent line y =
  8. calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)
  9. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals …
  10. Calculus AB

    Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?

More Similar Questions