Ex 2.68. find the stationary points on the curve y=3x^4 -4x³ -12x² +1 and determine whether they are maximum or minimum turning points

Answers

Answer 1

Answer: $y=3x^4 -4x^3 -12x^2 +1\ny'=12x^3-12x^2-24x\n\n12x^3-12x^2-24x=0\n12x(x^2-x-2)=0\n12x(x^2+x-2x-2)=0\n12x(x(x+1)-2(x+1))=0\n12x(x-2)(x+1)=0\nx=0 \vee x=2 \vee x=-1\n\n\forall{x\in(-\infty,-1)\cup(0,2)}\ y'<0\Rightarrow y\searrow\n\forall{x\in(-1,0)\cup(2,\infty)}\ y'>0\Rightarrow y\nearrow\n\Downarrow\ny(0)=1=y_(max)\ny(2)=3\cdot2^4-4\cdot2^3-12\cdot2^2+1=48-32-48=-32=y_(min)$
$y(-1)=3\cdot(-1)^4-4\cdot(-1)^3-12\cdot(-1)^2+1=3+4-12+1=-4=\n=y_(min)$

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Solve 2(x−5)^1/3=−16

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Answer:

x = − 19

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Simplify the expression 18 + 12xa 2 (9 + 5x )
b 3(6 +3x)
c 6 ( 3 + x)
d (3 + 2x)

Answers

Answer:

c:) 6(3 + 2x)

Step-by-step explanation:

The given expression is 18 + 12x. To simplify this expression, we can first look for any common factors that can be factored out. In this case, we can factor out 6, which gives:

18 + 12x = 6(3 + 2x)

So, the simplified expression 18 + 12x is 6(3 + 2x).

Factor 2x^3-12x^2+16x

Answers

Answer:

2x ( x-4) (x-2)

Step-by-step explanation:

What is 1/4 of 10 explain

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Too many points for such a simple explanation :)) Whatever:
To get 1/4 of a number you multiply the number by 1/4. Same for any non-percent number. If the number is a percent, say, 23,5%, you first divide it by 100 to get a non-percent, then do the same, that is, multiply it by the number.
Our result is $\frac{1}4*10=\frac{10}4=\frac{5}2=2\frac{1}2=2.5$

Plz help me with this

Answers

The answer would be 5(c+2) = 79
5*c= 5c
5*2= 10
5c+10=79

Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB?

Answers

the graph equation is in the form y = mx + c
we need to find m - gradient and c - intercept of the graph
since we have been given 2 points we know the x and y coordinates of these 2 points
point A , x = 0 and y = -4
point B , x = 6 and y = 2
substituting these x and y values in y = mx + c form
-4 = m*0 + c
-4 = c
then intercept is -4
substituting x and y in point B
2 = m * 6 + c
since c = -4
2 = 6m - 4
6m = 6
m = 1

since we know m=1 and c = -4
the equation for line AB is
y = 1*x - 4
y = x - 4

Answer: the answer is y + 4 = x

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