For the function f(x)= (x^2)-(4x)+6 on the interval [0,4]
What is the value of f(x) on [0,4]?
What is the value of f(x) on (0,4)?
If f(0)= f(4)= ?
By Rolle's Theroem, f '(c)=0
what does c=?
The given function is f (x) = x2 – 4x + 6 with the interval [0,4].
It is known that, the Rolle’s theorem states, If a real valued function f is continuous on a proper closed interval [a, b], differentiable on the open interval (a, b), and f (a) = f (b), then there exist at least one c in the open interval (a, b) such that f ’ (c) = 0.
By the above theorem, the function f (x) = x2 – 4x + 6 continuous on closed interval [0,4], and differentiable on the open interval (0,4).
Find the value of f (0) as follows.
f (0) = (0)2 – 4(0) + 6
= 0 – 0 + 6
Find the value of f (4) as follows.
f (4) = (4)2 – 4(4) + 6
= 16 – 16 + 6
=0 + 6
Thus, the both values f (0) and f (4) is 6.
It is given that, by Rolle’s theorem ...
Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*See Solution
Q: How can I get the result? Which is the result?
A: The function is given by,
Q: 21 If fx)3then f(x) O 2x-2-1 3x 2x-3r2-3 3x O 2x-3x2-3 6x 2x 3x+2 O 2x-x2-1
A: Find the derivative of the given function.
Q: please explain how to solve this
A: (a)We are given graphand we can locate upper and lower curves on different regions
Q: The equation abs(y/a)^n + abs(x/a)^n = 1, where n and a are positive real numbers. Make a complete ...
A: The equation abs(y/a)^n + abs(x/a)^n = 1,
Q: Let H(x)=4f(x) + 5g(x), where the graphs of f and g are shown in the figure. Find H`(1).
A: Firstly, we find the function y=f(x) , which is linear function , as it is a equation of straight ...
Q: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...
A: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...
Q: what are the steps to solving |x-4| > 9
A: We have to solve the inequality.Inequality is given below:
Q: Define R as the region bounded by the graphs of f(x)=x2 +2x+2, x=−2, x=0, and the x-axis. Using the ...
A: Click to see the answer
Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.
A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent wil...