Posted by Kara on Thursday, November 10, 2011 at 10:43pm.
Given the function defined as f(x)=x^3-(3/2)x^2-6x+10
a) Explain why f(x) must have a root between x=-3 and x=-2
b) Write an equation of the line perpendicular to the graph of f at x=0
c) Find the x and y coordinates of the point on the graph of f where the line tangent to the graph is parallel to the x-axis
Help would be GREATLY appreciated !
- Calculus - Damon, Friday, November 11, 2011 at 5:31am
The value of the function at x = -3 is
-27 -27/2+18+10 = -12.5
at x = -2 it is
-8 -12/2 +12+10 = 8
the function is continuous so must pass through zero on the way from -12.5 to +8
dy/dx = 3 x^2 -3x -6
at x = 0, dy/dx = -6
so slope of our line = +1/6
at x = 0, y = 10
so find equation of the line that passes through (0,10) with slope m = 1/6
dy/dx = 0 = 3 x^2 - 3x -6
x^2 - x - 6 = 0
(x-3)(x+2) = 0
so parallel to x axis at x = +3 and x = -2
find y at those points.
- Calculus - Anonymous, Wednesday, January 25, 2012 at 5:05pm
That is actually incorrect for the last part. The equation should turn out to be x^2-X-3. and then you should factor that to get x=-1 and x=2
Answer this Question
- Calculus - Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why ...
- calculous - 3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the ...
- Writing this equation - how do I write the equation of a line perpendicular to ...
- Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
- Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...
- Calculus - Let f be the function defined by f(x)=2x+11-3e^x If the equation of ...
- calculus - Find an equation of the line that is tangent to the graph f and ...
- Geometry - How do I write an equation of a line perpendicular to the graph of -...
- precalculus - Find (a) the equation of a line that is parallel to the given ...
- Algebra - graph the equation x-3=y (where do I plot the points?) find the ...