calculus
posted by james .
In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x<(1/4) f(x) is negative, for (1/4) <x<1 f(x) is positive, f(1/4)=0, f (2/3)=1, f ' (1/3)= 1, f ' (2/3) =3.
a. If the function G(x) is given by
G(x)= integral from 0 to x f(t) dt
what can you conclude about the maximum or minimum values of G on (0,1)?
b. What is the slope of the tangent line to G(x) at x=(2/3)?
>>>>please show steps<<<<

b. They tell you that the slope (f') there is 3.
Respond to this Question
Similar Questions

Math
a) Is âˆ«[1 to 1]e^x^3 dx positive, negative, or zero? 
Calculus
COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on the given interval? 
Calculus
COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on the given interval? 
Calculus
COnsider g(x)=(8)/(x6) on (6,13) (a) Is this function continuous on the given interval? 
Calculus
Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero on the interval (infinity, 0). So far this is what I have: 0=x^3 + 3/(x^2) +2 2= (1/x^2)(x^5 + 3) 2x^2= x^5 +3 But now I'm stuck. I also am not sure if this is … 
calculus
Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4. and f(x)= 6x, 4 < x <or= 6 a. Is f continuous at x=4? 
calc
Which of the following statements would always be true? 
Math11
Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? 
Calculus
Consider the function f(x) = {0, x = 0 and 1  x, 0 <= x <= 1}. Which of the following statements is false? 
Calculus
The function f is continuous on the closed interval [5,5], and f(2) = 6, f(1) = 3, and f(4) = 6. Which of the following statements must be true?