Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
11 dollars is I think what Ken or the kids name spent IDK
10 times 5 is 50
50 times 3.14 is 157.
157 cubic feet is the volume of this cylinder.
1 27/50 miles
18/25 multiply by 2 to get common denominator, then add 41/50 which gives you 77/50, then simplify.
Answer:
(6,1)
Step-by-step explanation:
Just look for the terms with x and y in them. Divide their coefficients by two, and multiply by -1. And then put them in an ordered pair.
So in this case, -12x --> 6 and -2y --> 1
Obviously the more orthodox way would be to actually complete the square, but I'm lazy, this way is faster, and since this seems to be multiple choice, as long as you have the correct answer, it shouldn't matter.