AP Calc part b

The function f has a first derivative given by f'(x)=x^4-6x^2-8x-3. In what intervals is the graph of f concave up?

A) (2,infinity) only

Let f be the continuous function for all real numbers. Let g be the function defined by g(x)=∫f(t)dt. If the average rate of change of g on the interval 2<x<5 is 6, which of the following statements must be true?

A) The average value of f on the interval 2<x<5 is 6.

A file is downloaded to a computer at a rate modeled by the differentiable function f(t), when t is time in seconds since the start of the download and f(t) is measured in megabits per second. Which of the following is the best interpretation of f'(5)=2.8?

B) At time t=5 seconds, the rate at which the file is downloaded to the computer is increasing at a rate of 2.8 megabits per second

x 1 2 3 4 5 f(x) 9 4 0 -3 -5 If f is twice differentiable on the interval 1<x<5 which is true?

B) f' is negative and increasing for 1<x<5

The function g is continuous of the closed interval [1,4] with g(1)=5 and g(4)=8. Which guarantees there is a number C in the open interval (1,4) where g'(c)=1?

B) g is differentiable on the open interval (1,4)

Let H(x) be an antiderivative of (x^3+ sinx)/(x^2+2). If H(5)=pi, then H(2)=?

B)-5.867

let f be the function f(x)= ln(x^2+1), let g be g(x)= (x^5+x^3). The line tangent to the graph of f at x=2 is parallel to the line tangent to the graph of g at x=a, where a is a positive constant. What is a?

C) 0.447

let f be a function with derivative given by f'(x)=(x^3-8x^2+3)/(x^3+1) for -1<x<9. At what value of x does f attain a relative max?

C) 0.638

The continuous function f is positive and has domain x>0. If the asymptotes of the graph of f are x=), y=2. What is true?

C) Lim as x->0 f(x)= infinity and f(x)=2

A particle travels along a straight line with velocity v(t)= (3e^(-t/2))sin(2t) mps. what is the total distance in meters, traveled by the particle during the time 0<t<2?

D

the number of bacteria in a container increases at the rate of r(t) bacteria per hour. If there are 1000 bacteria at time t=0, which gives the number of bacteria at t=3 hours?

D) 1000+ 0∫3 R(t)dt

The graph of a differentiable function f is shown. Which is true?

D) f'(3)<f'(0)<f'(-2)

for any function f, which statement is true?

II and III only (if f is continuous at x=a, then lim as x->a f(x)=F(a), f is differentiable at x=a, then lim as x->a f(x)= f(a))

f''(x)=x(x-1)^2 (x+2)^3 g''(x)=x(x-1)^2 (x+2)^3+1 h"(x)= x(x-1)^2 (x+2)^3-1 The twice differentiable functions f,g,h have second derivatives given above. What functions have a graph with 2 points of inflection?

f and g only

The graph of the function f is shown above for -2<x<2. Which of the following could be the graph of an antiderivative f?

not C, idk which