calculus
posted by Mike .
The graph of f'(x) is shown for 0=< x =<10. The areas of the regions between the graph of f' and the xaxis are 20, 6, and 4, respectively.
I'm going to describe the graph of f' since I can't post pictures. The first section of the graph goes up (like the sin function) and the area underneath it is 20. Then, it decreases below the xaxis and increases above the xaxis, and the area underneath it is 6. The graph then increases and decreases onto the xaxis, and the area underneath it is 4.
What is the maximum value of f on the closed interval [0,10] of f(0) = 2?
The answer is 22, but I don't know how to get it.

Calculus 
Jason
To answer the question you would be looking at the point in the interval 0 < x < 10 which the area's totaled up is greatest.
The point at which the area is greatest is the interval in which the area is 20, if you span it all the way towards x=10, you'd have (206+4 = 18) which is clearly lower than 20.
Also the question includes that f(0) = 2, meaning you have an extra +2 to add.
Therefore the greatest maximum value that can be made is the 20 + 2 = 22.
Respond to this Question
Similar Questions

Calc
a partial moves along the xaxis so that its velocity at time t, for 0< = t = < 6, is given by a differentiable function v whose graph is shown above. The velocity is 0 at t=0, t=5, and the graph has horizontal tangents at t=4. … 
help math
a partial moves along the xaxis so that its velocity at time t, for 0< = t = < 6, is given by a differentiable function v whose graph is shown above. The velocity is 0 at t=0, t=5, and the graph has horizontal tangents at t=4. … 
calculus
let f be the function f(x) = x^3 + 3x^2  x + 2 a. the tangent to the graph of f at the point P = (2,8) intersects the graph of f again at the point Q. Find the coordinates of point Q. b. Find the coordinates of point R, the inflection … 
calculus
a particle moves along the xaxis (units in cm) its initial position at t=0 sec is x(0)=15. the figure shows the graph of the particle's velocity v(t). the numbers are areas of the enclosed regions. in the graph 0 to a is 4 under the … 
calculus
Given the graph of f(x) find the graph of 2 f( 3x  2)  4 Is this correct? 
calculus reposted
Given the graph of f(x) find the graph of 2 f( 3x  2)  4 Is this correct? 
College Algebra
1.Answer the following for the given quadratic function. f(x) = 2x^2  8x  13 (a) does the graph of f open up or down? 
Physics
How do you convert a distance time graph to a velocity time graph. In my first distance time graph, i have 3 curves, two are above the x axis the the middle curve is under the x axis. i am confused on how to change this graph into … 
PreCalculus
Hello! I need help with these 2 questions: 1.) Describe how the graphs of f(x) = 2x and g(x) = 2x are related. a.) All of these. b.) The graph of g(x) is a reflection of the graph of f(x) over the yaxis. c.) Non of these. d.) … 
PreCalc
1.) Describe how the graphs of f(x) = 2x and g(x) = 2x are related. a.) All of these. b.) The graph of g(x) is a reflection of the graph of f(x) over the yaxis. c.) Non of these. d.) The graph of g(x) is a reflection of the graph …