Answer:
1 and 2) After multiplying (x+y+3)(y+1) we have
Which is an equivalent expression after applying the distributive property.
As we can see we have an one of the variables squared, so we obtain an Parabolic Cillinder
<span>a) Intervals of increase is where the derivative is positive
b) </span> <span>Intervals of decrease is where the derivative is negative. </span>
c) <span>Inflection points of the function are where the graph changes concavity that is the point where the second derivative is zero </span>
<span>d)
Concave up- Second derivative positive </span>
<span>Concave down- second derivative negative </span>
f(x) = 4x^4 − 32x^3 + 89x^2 − 95x + 31
<span>f '(x) = 16x^3 - 96x^2 + 178x - 95 </span>
<span>f "(x) = 48x^2 - 192x + 178 </span>
<span>By rational root theorem the f '(x) has one rational root and factors to: </span>
<span>f '(x) = (2x - 5)*(8x^2 - 28x + 19) </span>
<span>Using the quadratic formula to find it's two irrational real roots. </span>
<span>The f "(x) = 48x^2 - 192x + 178 only has irrational real roots, use quadratic formula which will be the inflection points as well.</span>
(5+8)x(6-2)+5 The brackets go there because of the way the numbers are placed. (I added words because without them I could not post this answer.)
Given that Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second.
An olympian ran the 100-meter dash in 9.6 seconds.
Then speed of olympian = distance/ time = 100 meter/ 9.6 seconds = 100 meter/ 9.6 seconds = 10.4166666667 meter/ seconds
whis is approx 10.42 meter/seconds
Now we need to find about how much faster was Sarah the cheetah’s speed, to the nearest tenth of a meter per second.
16.8-10.42 = 6.38 = 6.4
Hence speed of Sarah the cheetah's is approx 6.4 meter per second more than the speed of olympian.
