Simplify the following expression: (3x+4)(x-1)(x-3)
2 answers:
Answer:
3x³ - 8x² - 7x + 12
Step-by-step explanation:
We multiply these terms, (so expand the brackets). Referring to the diagram attached, we multiply the first terms, outer terms, inner terms, and last terms.
Let's first look at the first two (we will do something about the third brackets later):
(3x+4)(x-1)
Firsts:
3x²
Outer:
-3x
Inner:
4x
Last:
-4
Now we combine:
3x² - 3x + 4x - 4
= 3x² + x - 4
So from the whole equation, we now have this:
(3x² + x - 4)(x - 3)
We do a similar thing here.
3x³ - 9x² + x² - 3x - 4x + 12
Simplify:
3x³ - 8x² - 7x + 12
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Answer:
No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R
Step-by-step explanation:
Assuming: the function is in [0,1]
And rewriting it for the sake of clarity:
Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer
1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:
2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]
The limit to the left
g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)
3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R
Because this is the same as to calculate the limit from the left and right side, of g(x).
This is what the Bilateral Theorem says: