Posted by Joan on Wednesday, April 20, 2011 at 7:59pm.
The function f is continuous on the closed interval [0,2] and has values that are given in the table below
x = 0 1  2
____________
f(x) = 1 k  2
The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if K = ?
The answer is 0, but there is also a choice option of 1/2. I don't understand how to get the answer.
Thanks!

calculus  MathMate, Thursday, April 21, 2011 at 3:46pm
For f(x)=1/2 to have two solutions on the interval [0,2], a horizontal line through y=1/2 must intersect f(x) two times or more on the interval.
This will happen if k<=1/2. In the limit where k=1/2, the horizontal line will be tangent to f(x), and is considered to have two solutions.
Answer This Question
Related Questions
 Calculus IVT  The function f is continuous on the closed interval [0,6] and has...
 calculus  The function f is continuous on the closed interval [0,6] and has ...
 Calculus  The function f is continuous on the closed interval [1,7] and has ...
 Calculus  The function f(x)=(x^4)(10x^3)+(18x^2)8 is continuous on the closed...
 Calculus  The function f is continuous on the interval [4, 15], with some of ...
 Calculus  COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on ...
 Calculus  COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on ...
 Calculus  COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on ...
 Calculus  I am doing the AP calculus review, these are the questions I have no ...
 AP Calculus AB  The function f is continuous on the interval [4, 15], with some...
More Related Questions