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A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 19 ft/sec2. Calculate how far the car travels in the time it takes to stop. Round your answer to one decimal place. Please give units with answer.

A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2. How long before the car stops? Round your answer to one decimal place. Please explain and give units with answer

Find the second derivative of f(x) = x^3 + x^4 and its sign chart. Which of the following is not true about f? I know the second derivative is 12x^2+6x but i am a little confused because it asks about f not f'. 

A) f is concave down on (-1/2, 0)

B) f is concave up on (-∞, -1/2) U (0, ∞)

C) f is concave up on (-1/2, 0)

D) f has inflection points at x=-1/2 and x= 0.

E) All are not true. 

Let f′(x) = 100x(2x+3)(x−5).Use sign chart to determine the interval(s) on which f is increasing or decreasing

For f(x)=1+x+x2. Use the Mean Value Theorem to show that there is a real number c, 0<c<2, such that f(2)−f(0)=f′(c)(2−0).

x^2+(xy)^2+y^3=100

Given f(x)=(x^2+x−2)/(x^2−3x−4) , List all important features of the graph: local maxima and minima, inflection points, and asymptotic behavior. 

Assume that f is a polynomial and x=10 is a critical number for f.

If   f′′(10)=−2–√, 

 what do we conclude from the Second Derivative Test?

A. f has a local maximum at x=10

B. f has a local minimum at x=10

C. f has inflection point at x=10

D. f is concave up for x>10

E. f is concave down for x>10

The function given below satisfies the Mean Value Theorem on the specified interval. Find the value of c in the interval (1,2) where

f′(c) = f(b)−f(a)/

        b−a

f(x)=x^3−1.7x;[1,2]

Let A be the area of a circle with radius r that is increasing in size with respect to time. If the rate of change of the area is 3 cm/s, find the rate of change of the radius when the radius is 6 cm.

You have 800 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what is the dimension of the rectangular pen that maximizes the area?

f(x)= (g(x))^3

g(5)=-3, g'(5)= 6

f'(x) = 3(g(x))^2 * g'(x)

f'(5) = 3(g(5))^2 * g'(5) = what?

I have solved and got 75 that is wrong, 30 is wrong, and 225 is wrong. Can someone please explain how to solve?

The position function s(t)=t^3−8t gives the position in miles of a freight train where east is the positive direction and t is measured in hours.

a. Determine the direction the train is traveling when s(t)=0 .

b. Determine the direction the train is traveling when a(t)=0 .

c. Determine the time intervals when the train is slowing down or speed up. 

find slope of tangent line mtan=f'(a), and find the equation of the tangent line to f at x=a