<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:
A 4^-2
Step-by-step explanation:
(4^3 * 4^-2) -2
(4^3-2)-2
(4^1)-2
4^-2
Answer: D
Step-by-step explanation:
Step-by-step explanation:
Given,
Base of the triangle
Hypotenuse of the triangle = 5
Height of the triangle = x
Therefore, According to Pythagoras Theorem,
Hence, the required value of <u>x is 1.</u>
Answer:
4.48
Step-by-step explanation:
4.00 + 12%(.48)= 4.48