My question is how long does it take her to make 1 CD
To find concavity we need to find the second derivative.
Use quotient rule to find f'(x)=4/(x+3)^2
Then use chain rule to find f''(x)=-8/(x+3)^3
To find potential inflection points, we need to find all x values where the second derivative is equal to 0 or is undefined.
Set the numerator and denominator equal to 0 and solve.
(x+3)^3=0
x+3=0
x= -3
Now plug a value less than -3 and greater than -3 into the second derivative to find where the concavity is upward (positive number).
Since f''(-4) is positive, that means that f(x) is concave up on the interval (-infinity, -3).
His displacement ... the distance between his start point and
his end point ... was 10 miles. But we don't know what route
he followed on the way, so we don't know how much distance
he actually walked or drove. It couldn't be less than 10 miles,
but it could be any distance more than 10 miles.
