Math help asap for brainleist
1 answer:
a. The slope between (-3, 0) and (0, -1) is: -1/3.
b. The slope between (1, -4) and (-7, 4) is: -1.
c. The relationship is not linear.
<h3>How to Calculate the Slope?</h3>We can find the slope of a relationship that is represented by a table of values by using two points from the table, then apply the formula below:
Slope (m) = change in y/change in x = .
Part A: Using two points from the table, (-3, 0) and (0, -1)
Slope (m) = change in y / change in x = (-1 - 0) / (0 - (-3))
Slope (m) = -1/3
Part B: Using another two points, say (1, -4) and (-7, 4)
Slope (m) = change in y / change in x = (4 - (-4)) / (-7 - 1)
Slope (m) = 8/-8
m = -1
Part C: The slopes from part A and part B are not the same or constant, this shows that the relationship between the points is not linear.
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(a) It looks like you're saying
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)