<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>
Answer:
1.) rectangle and triangle
2.)4 because 2 for each rectangle
3.)yes and a rectangle has 4 vertics and 4 sides and 2 equal lengths
Pick one coordinate point on figure 1 (-4,5)
First rotate 90 degree clockwise rule (x,y) -->(y , -x)
So (-4,5) rotate 90 degree clockwise will become (5, 4)
Then reflection over x a-xis, rule (x,y) -->(x,-y)
So (5, 4) reflection over x a-xis will be (5, -4)
Answer: first option
90 clockwise rotation around the origin, then a reflection across x - axis.
Hope it helps
(-x-1)(x-1)(x^2+6)
distribute from there i think?
math papa website can help with this... im not that good at math
