Posted by nick on Sunday, September 30, 2007 at 7:01pm.
The function f is defined by
f(x) = x^3  x^2  4x + 4
The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, 8) which is not on the graph of f. Find the values of a and b.
I have no clue how to solve this
I know the derivative of f prime (x) is
3x^2  2x  4 and so (a,b) would be on the derivative line and so would (0, 8) but how do i find (a,b)???

calc  drwls, Sunday, September 30, 2007 at 7:23pm
The equation of the tangent line is
y = mx 8,
where m is the slope at the tangent point (a,b).
At (a,b), the value of y is
a^3  a^2 + 4a + 4 = b
and the slope is
dy/dx @ x=a =
3x^2 2x 4 = 3a^2 2a 4 = m
From the tangent line equation, we also know that, at (a,b)
b = m a 8
So there are 3 equations in the three unknowns, m, a and b.
It is a bit messy, but that is as far as I can go.
Answer This Question
Related Questions
 Calculus  1. Given the function f defined by f(x) = x^3x^24X+4 a. Find the ...
 calculus  The function f is defined by f(x) = x^3  x^2  4x + 4 The point (a,b...
 math, a.p. calc  Let g be a function that is defined for all x, x ≠ 2, ...
 Calculus  Sketch a graph of the parabola y=x^2+3. On the same graph, plot the ...
 Math calculus  Given f(x) = x ^ 3  x ^ 2 4x +4 Find the zeros of f. Write an...
 Calculus  Functions?  #1. A cubic polynomial function f is defined by f(x) = ...
 Calculus  Graph the function f(x)=x+4/x Graph the secant line that passes ...
 calculus  find a function f given that (1) the slope of the tangent line to ...
 cal  Equations of the tangent lines to hyperbola xy=1 that pass through point...
 Calc  Write the equation of the line tangent to the graph of the function at ...
More Related Questions