Find the maximum and minimum point for y=3+4x³-x⁴. Sketch the graph of the curve.
1. Find the maximum and minimum point for y=3+4x³-x⁴. Sketch the graph of the curve.
Jawab:
Penjelasan dengan langkah-langkah:
[tex]y = 3+4x^3 - x^4\\\\y' = 12x^2 - 4x^3 = 0\\\\x^3 - 3x^2 = 0\\\\x^2(x-3) = 0\\\\x = 0 \;\cup\; 3\\\\y'' = 24x - 12x^2 = 0\\\\x^2 - 2x = 0\\\\x(x-2) = 0\\\\x = 0 \;\cup\; 2\\\\y''' = 24-24x = 0 => x = 1\\\\ y'''' = -24\\\\\begin{minipage}{15em}berdasarkan turunan keempat, ketiga, kedua, dan pertama :\\\\- f(x) terbuka keatas dan memiliki minimum pada interval $0 < x < 2$ \\\\- f(x) terbuka kebawah dan \\memiliki maksimum pada \\interval $x < 0$ atau $x > 2$ \\\\\end{minipage}[/tex]
[tex]\begin{minipage}{15 em}- f(x) memiliki perubahan kecekungan parabola singgung terbesar pada x = 1\\\\- berdasarkan turunan kedua maka f(x) memiliki maksimum lokal di x = 3\\\\- x = 0 pada interval $ 0< x < 2 $ bukan merupakan maksimum maupun minimum, tetapi secara keseluruhan tanpa interval x = 0 merupakan minimum f(x) (karena maksimum f(x) sudah ditemukan)\end{minipage}[/tex]
[tex]\begin{minipage}{15 em}- Nilai turunan keempat negatif dan mempengaruhi sifat turunan diatasnya \\- f(x) monoton turun ketika $x > 3$ dan monoton naik untuk \\$x < 0 \;\cap\; 0<x<3$ \\(netral pada x = 0)\end{minipage}[/tex]
maximum = f(3), "minimum" = f(0) = 3 = titik potong sumbu y
maximum = 3+4(3)³ - 3⁴ = 30
2. 5. The points (4, a), (5,-2) are some points on the graph of y = 2x + 7. Find without plotting the graph, (a) the value of a, (b) the value of b.
Penjelasan dengan langkah-langkah:
(4, a) ------> y = 2x + 7
a = 2 . 4 + 7
= 8 + 7
= 15
so, value of a is 15
3. Diagram 5 shows the graph of a quadratic function y = f(x)
a. y = 21+4x-x²
0 = 21+4x-x²
0 = (7-x)(3+x)
x = 7 atau x = -3
b. mencari sumbu simetri di turunan pertama:
y = 21+4x-x²
y' = 4 - 2x ; subtitusi y' = 0 (karena pada titik puncak, m=0)
0 = 4 - 2x
2x = 4
x = 2 ← sumbu simetri
4. the graph of y = ax2 bx c has its vertex at the point (1, 5) and intersects the y-axis at (0, 1). find the values of a, b and c
Jawaban:
a = –4, b = 8, and c = 1.
Pembahasan
Fungsi Kuadrat (Quadratic Functions)Given that the vertex of y = ax² + bx + c is (1, 5), we know that the axis symmetry for this graph is x = 1, which equals to –b/(2a).
Therefore:
–b/2a = 1
⇔ b = –2a ....(i)
From that vertex, we know that y = 5 when x = 1. The value of y is the minimum or maximum value of ax² + bx + c.
Let’s substitute –2a for b, based on eq. (i).
y = ax² – 2ax + c .....(ii)
And then, substitute 5 for y and 1 for x.
5 = a(1²) – 2a(1) + c
⇔ 5 = a – 2a + c
⇔ 5 = –a + c
⇔ c = a + 5 .....(iii)
Substitute a + 5 for c in eq. (ii).
y = ax² – 2ax + a + 5 .....(iv)
The y-intercept point is at (0, 1).
Let’s plug x = 0 and y = 1 into eq. (iv).
1 = a(0²) – 2a(0) + a + 5
⇔ 1 = 0 – 0 + a + 5
⇔ 1 = a + 5
⇔ a = 1 – 5
⇔ a = –4
Plug a = –4 into eq. (i), we get:
b = –2(–4) = 8
And then, plug a = –4 into eq. (iii), we get:
c = –4 + 5 = 1
CONCLUSIONa = –4, b = 8, and c = 1.
The complete function is y = –4x² + 8x + 1.
5. which graph represents the solution of the inequality -12x > 36
Jawaban:
the working and the answer are shown in the pic.
semangat belajar;))
6. What is y- intercept point of the graph below?
Jawaban:
(0,-6)
Penjelasan dengan langkah-langkah:
ingat bahwa y- intercept point (titik potong sumbu y) adalah titik yang memotong sumbu y (vertikal) dan titik bertemunya garis di x=0
lokasinya pada fungsi kuadrat adalah (0,c)
misal...
x² - 2x + 3
a = 1
b = -2
c=3
maka titik potong sumbu y adalah (0, 3)
--------
di grafik, titik potong sumbu y berada di (0,-6)
7. Which part of the bar graph shows the name of the graph?a. Titleb. Axisc. Scaled. Labelsmaaf bukan mata pelajaran indonesia kepencet harusnya matematika
Pertanyaan
Which part of the bar graph shows the name of the graph?
a. Title
b. Axis
c. Scale
d. Labels
Jawaban:
d. Labels
Penjelasan:
maaf kalo salah
semoga membantu
8. the graph of x + y = -4 passes through Y-axis at the point (0, k) and passes through X-axis at the point (h, 0). what is the value of k and h?
melewati Y axis (0,k)
0 + k = -4
k = -=
melewati X axis (h,0)
h + 0 = -4
h = -4
9. If y is directly proportional to x and y = 20 whenx = 5,(i) find an equation connecting x and y,(ii) draw the graph of y against x.
diketahui [tex]x\propto y[/tex]
maka [tex]x = ky[/tex]
dengan [tex]k[/tex] suatu konstanta
berdasarkan yang diketahui
[tex]20 = k\cdot 5[/tex]
bisa didapat bahwa
[tex]k = 4[/tex]
sehingga
(i) [tex]y = 4x[/tex]
10. Choose the correct form of the verbs
Jawaban:
1. Plays
2. Live
3. Like
4. Works
5. Study
6. Surfs
7. Plays
8. Go
9. Goes
10. Loves
Penjelasan:
MAAFKLOSALAH!!!!:(Jawaban:
1. Ben plays football everyday
2. They live in Paris
3. Jane and I like dancing
4. My mum works in a bank
5. We study English at school
6. Joe surfs the net every day.
7. My sister plays the piano
8. I go to bed at ten o'clock.
9. Jane goes to school by bike.
10. He loves Leah
Penjelasan:
Tenses yang digunakan adalah simple present.
Form = S + V1/Vs +...
Kalau He, She, It menggunakan Vs kalau They, We, I, You gunakan V1
kalau ada salah maaf ya :)
11. Draw the graph of y =2x-7 and find its gradient
Jawab:
Penjelasan dengan langkah-langkah:
12. mohon bantuannya The picture is a graph of quadratic function......
Persamaan umum fungsi kuadrat :
f(x) = Ax² + Bx + C
Diketahui grafik fungsi f(x) melewati titik :
» (3 , 0)
=> f(3) = 0
=> A.(3)² + B.(3) + C = 0
=> 9A + 3B + C = 0 ( i )
» (–1 , 0)
=> f(–1) = 0
=> A.(–1)² + B.(–1) + C = 0
=> A - B + C = 0 ( ii )
» (0 , 3)
=> f(0) = 3
=> A.(0)² + B.(0) + C = 3
=> C = 3
Subtitusikan nilai C ke ( i ) :
9A + 3B + C = 0
9A + 3B + 3 = 0
9A + 3B = –3 ( iii )
Subtitusikan nilai C ke ( ii ) :
A - B + C = 0
A - B + 3 = 0
A - B = –3 ( iv )
Eliminasi ( iii ) dan ( iv ) :
( iii ) : 9A + 3B = –3
(iv) × 3 : 3A - 3B = –9
________________ +
12A = –12 => A = –1
Subtitusikan nilai A ke ( iv ) :
A - B = –3
–1 - B = –3 => B = 2
Substitusikan nilai A, B, dan C ke persamaan fungsi kuadrat :
f(x) = Ax² + Bx + C
f(x) = (–1)x² + (2)x + (3)
Jadi, persamaan fungsi kuadrat grafik tersebut adalah : f(x)=–x²+2x+3
13. Which of the following statements correctly describes the motion of the car shown by the velocity time graph
Mana dari pernyataan-pernyataan berikut benar menjelaskan gerakan mobil yang ditunjukkan oleh kecepatan waktu grafik.
14. Choose a graph from below, and write a description using the information in the graph. *tolong deadline hari ini:))
Jawaban:
Maaf kalo salah
Penjelasan:
In the beginning of 2010, during january to August, the salmon catches were higher than the trout catches. but at September, the trout catches overtook the salmon catches
15. Find the vertex in the graph of y = 3x^2 – 12x + 2. pls bantu (jgn ngasal)
Penjelasan dengan langkah-langkah:
vertex ---> sumbu simetri
y = 3x² - 12x + 2
dengan a = 3, b = -12, c = 2
maka
sumbu simetri x = -b/2a
x = -(-12)/(2)(3)
x = 12/6
x = 2
16. make the graph of this equation : 2x + y = 2!
Semoga Bermanfaat
:")
17. Tuliskan graph y = sin 4x
grafik seperti pada gambar
Semoga membantu
18. which graph represents the solution of the inequality -12x > 36
Jawaban:
the working and the answer are shown in the pic.
semangat belajar;))
19. The line graph shows the number of cans of baked beans a machine sealed over five minutes
Jawaban:
a) 128 cans
b) 128÷4 = 32 cans
c) 480 cans ÷ 32 = 15 minutes
20. Find the area under the graph of fx=4x3-3x2+4x+2 Between x=1 and x=2.
Jawab:
16 units²(16 satuan luas)
Penjelasan dengan langkah-langkah:
The image of how to solve the area under the curve, is shown below!
___________
#StayPositive - kexcvi
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