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
The surface area will increase by a factor of 49/16
To find the answer to the question we do the equation
Which gets us our answer of 20%
The standard form for the equation of a circle is :
<span><span><span> (x−h)^</span>2</span>+<span><span>(y−k)^</span>2</span>=<span>r2</span></span><span> ----------- EQ(1)
</span><span> where </span><span>handk</span><span> are the </span><span>x and y</span><span> coordinates of the center of the circle and </span>r<span> is the radius.
</span> The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter with endpoints at (−10,1)and(−8,5) is :
((−10+(−8))/2,(1+5)/2)=(−9,3)
So the point (−9,3) is the center of the circle.
Now, use the distance formula to find the radius of the circle:
r^2=(−10−(−9))^2+(1−3)^2=1+4=5
⇒r=√5
Subtituting h=−9, k=3 and r=√5 into EQ(1) gives :
(x+9)^2+(y−3)^2=5
Answer:
0333
Step-by-step explanation:
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11122222 ans
