Which of the following symbols is drawn as a dashed/dotted line? 1.) 2.) > 3.) = 4.) >/
1 answer:
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Answer:
Step-by-step explanation:
you can find where the first derivative is 0 to find the critical points
g'(x) = ( x^4 -5x^2 +4)' = 4x³-10x
g'(x) =0, make y =0 to find find where g'(x) is 0
4x³-10x =0 , factor 2x
2x(2x²-5)= 0 , each factor must be 0
2x= 0, so x= 0
2x²-5 =0, so x = ±√5/2
we now have 3 critical points -√5/2, 0, and √5/2
make intervals (-∞, -√5/2), (-√5/2, 0) , (0, √5/2) and (√5/2, +∞)
pick a point to test on each interval: -2, -1, 1 and 2 for example, and
calculate g'(x) = 4x³-10x at those points
for x= -2 we have 4(-2)³-10(-2) = -12 , negative number, decrease
for x= -1 we have 4(-1)³-10(-1) =6, positive number, increase
for x= 1 we have 4(1)³-10(1) = -6, negative number, decrease
for x= 2 we have 4(2)³-10(2) = 12, positive number, increase
we went from a decrease to an increase on intervals (-∞, -√5/2), (-√5/2, 0) so x= - √5/2 ≈ -1.58 is a minimum
we went from a decrease to an increase on intervals (0, √5/2), (√5/2, +∞) so
x= √5/2 ≈ 1.58 is a minimum as well
Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2,3)
m = =
= 2 , thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 3), then
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = 2x - 1 ← equation of line