<span> (x-1) (x+4) hope this helps</span>
Answer:
range means finding the slope value of the graph. :)
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Product to Sum Identities:
2 sin A sin B = cos (A - B) - cos (A + B)
2 sin A cos B = sin (A + B) + sin (A - B)
Use the Unit Circle to evaluate: cos 120 = -1/2 & sin 60 = √3/2
<u>Proof LHS → RHS</u>
LHS: sin 20 · sin 40 · sin 80
Regroup: (1/2) sin 20 · 2 sin 40 · sin 80
Product to Sum Identity: (1/2) sin 20 [cos(80-40) - cos (80+40)]
Simplify: (1/2) sin 20 [cos 40 - cos 120]
Unit Circle: (1/2) sin 20 [cos 40 + (1/2)]
Distribute: (1/2) sin 20 cos 40 + (1/4) sin 20
Product to Sum Identity: (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20
Simplify: (1/4)[sin 60 + sin (-20)] + (1/4) sin 20
= (1/4)[sin 60 - sin 20] + (1/4) sin 20
Unit Circle: (1/4)[(√3/2) - sin 20] + (1/4) sin 20
Distribute: (√3/8) - (1/4) sin 20 + (1/4) sin 20
Simplify: √3/8
LHS = RHS: √3/8 = √3/8
Calculation of relative maxima and minima of a function f (x) in a range [a, b]:
We find the first derivative and calculate its roots.
We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:
f '' (a) <0 is a relative maximum
f '' (a)> 0 is a relative minimum
Identify intervals on which the function is increasing, decreasing, or constant. G (x) = 1- (x-7) ^ 2
First derivative
G '(x) = - 2 (x-7)
-2 (x-7) = 0
x = 7
Second derivative
G '' (x) = - 2
G '' (7) = - 2 <0 is a relative maximum
answer:
the function is increasing at (-inf, 7)
the function is decreasing at [7, inf)