<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>
The correct solution is
CSubtract 6 from both sides of the equation
3x + 6 - 6 = 21 - 6
3x = 15
Then divide both sides by 3
x = 5
A:12/3 = -4
b:-12/3 = -4
c:-12/-12 = 4
e:-5/5 = -1
f:5/-5 = -1
g:-5/-5 = 1
Answer:
x = 2 - sqrt(19/6)
x = 2 + sqrt(19/6)
Step-by-step explanation:
12y+ 34=8
-34. -34
12y/12= -26/12
Y= -2.16
