What is the sign of −4ab when a>0 and b<0?
1 answer:
Answer:
A
Step-by-step explanation:
We have the expression:
And we want to find its sign given that a>0 and b<0.
Notice that the expression is already negative since we have -4.
a>0 means that a is positive. Therefore, we can ignore it since it won’t do anything.
b<0 means that b is negative. Therefore, we will have two negatives being multiplied together. Hence, this will make a positive.
Therefore, the sign of our expression will be positive.
We can see this with an example. Let a=1 (1>0) and let b=-1 (-1<0). Then:
So, the sign is positive.
Hence, the answer is A.
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Answer:
1/4
Step-by-step explanation:
The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.
The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...
(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4
