Which equation represents the word sentence shown below?
2 answers:
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To find the tangent line we will need the slope of the tangent at x=-1 (the x-coordinate of the point given). We find the slope by using the derivative of the curve.
Th curve given is
which can be solved for y by taking the root of both sides. We obtain 
We find the derivative using the chain rule. Bring down the exponent, keep the expression in the parenthesis, raise it to 1/2 - 1 and then take the derivative of what is inside.
Next we evaluate this expression for x=-1 and obtain:
So we are looking for a line through (-1,2) with slope equal to -9/2. We use y=mx+b with m=-9/2, x=-1 and y=2 to find b.
2-(9/2)=b
b=-5/2
So the tangent line is given by y=(-9/2)x+(-5/2)
Th curve given is
We find the derivative using the chain rule. Bring down the exponent, keep the expression in the parenthesis, raise it to 1/2 - 1 and then take the derivative of what is inside.
Next we evaluate this expression for x=-1 and obtain:
So we are looking for a line through (-1,2) with slope equal to -9/2. We use y=mx+b with m=-9/2, x=-1 and y=2 to find b.
2-(9/2)=b
b=-5/2
So the tangent line is given by y=(-9/2)x+(-5/2)