Question

I also have these other four question I need help on please!!

1. The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(4) = 6, evaluate f(0).

A. -2
B. 2
C. 4 <--- My choice
D. 10




2. The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false?

A. The graph of f has an inflection point at x = 0.
B. The graph of f has a relative maximum at x = 0.
C. The graph of f is always concave down.
D. The graph of the second derivative is always negative.


3. f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f '(x). What is the value of g '(0.1)?

x 0.1 0.2 0.3 0.4 0.5
f '(x) 1 2 3 –4 5

A. -16 <----- My choice
B. -4
C. 4
D. Cannot Be Determined


4. The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.

Using a left Riemann sum with 5 subintervals, estimate the total amount of water consumed in that time interval.

x 0 2 5 7 11 12
f(x) 5.7 5.0 2.0 1.2 0.6 0.4


A. 22.1
B. 34.8
C. 35.8
D. None of these


THANK YOU!!! :)

Answer 1

Anybody know how I can provide the image/ link for question 1 without being blocked by Jiskha?

Problem 1 shows a specific graph for the problem.

Answer 2

I reworked my process for number 1 and I got B. 2 this time. Is that correct?

Answer 3

#1. No idea
#2. A - consider y = -x^2
#3. Looks good
#4
x 0 2 5 7 11 12
f(x) 5.7 5.0 2.0 1.2 0.6 0.4
the left sum is, of course,
5.7*2 + 5.0*3 + 2.0*2 + 1.2*4 + 0.6*1 = 35.8

Answer 4

It is 2