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Ymorist [56]
2 years ago
14

Consider the curve y = x − x3. (a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of

the tangent line in part (a).

Mathematics
1 answer:
Katena32 [7]2 years ago
7 0

Answer:

a) mt = -2

b) y=2-2x

Step-by-step explanation:

We have y=x-x^{3}  ⇒  f(x)=x-x^{3} and we must find

a) The slope of the tangent line to the curve at the point (1,0)

b) The equation of the tangent line in part (a)

a) f(x)=x-x^{3} with the point (1,0) then f'(x) =1-3x^{2} the slope (mt) in x=1 is

f'(1)=1-3(1^{2})=1-3=-2  ,  m t= -2

b) mt=-2 at the point (1,0), knowing that the pending point model  is:

y-y_{1}=m(x-x_{1}), we solve y-0 = -2(x-1) ⇒ y=-2x+2

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Debora [2.8K]

Option A

2x^2(6x-1) + 3(6x-1) is one way to determine the factors of 12x^3-2x^2+18x-3 by grouping

<em><u>Solution:</u></em>

Factoring by grouping means that you will group terms with common factors before factoring

<em><u>Given expression is:</u></em>

12x^3-2x^2+18x-3

Group the first two terms together and then the last two terms together.

(12x^3-2x^2)+(18x-3)

We can see that 2x^2 is common in first two terms

And 3 is common in last two terms

Factor them out

(12x^3-2x^2)+(18x-3) = 2x^2(6x-1) + 3(6x-1)

2x^2(6x-1) + 3(6x-1)

Thus option A is correct

6 0
2 years ago
Read 2 more answers
A ball is thrown down from a balcony with a vertical velocity (in ft/s) given by
fenix001 [56]

Answer:

–90 < –32t – 10 < –58

Step-by-step explanation:

We want the velocity to be BETWEEN -90 and -58.

Whenever we need a quantity, let it be A, to be between two numbers, p and q (p is less than q), we can write it as:

p < A < q

Similarly, here we need the velocity, -32t-10 to be BETWEEN -90 and - 58 (with -90 being the smaller number). Thus we can write:

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This is the correct choice, 2nd choice.

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Answer:

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Step-by-step explanation:

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Therefore, the answer is B)

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