Find an equation to the tangent line...

label Algebra
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Find an equation of the tangent line to the curve 
y = x sqrt x
 that is parallel to the line 

y = 3 + 3x

May 6th, 2015

y = 3x + 3, we know that the slope is 3 because the line is in the form y = mx + b, where m is the slope

parallel lines have equal slopes so from the straight line equation the gradient of the tangent must be 3.

y=x sqrt x= x*x^(1/2)=x^(3/2)

dy/dx=3/2x^(1/2)

3=3/2x^(1/2)

2 = sqrt(x) 
4 = x 

so now we know that the tangent line hits the curve at x = 4. plug that into the original to find the y - value 

y = 4(sqrt(4)) 
y = 4(2) = 8 

So the point on the curve is (4,8). 

Use the linear formula: y-y1=m(x-x1)

y-8=3(x-4)

y-8=3x-12

y=3x-4

answer the tangent line to the curve y = x sqrt x is y=3x-4


May 6th, 2015

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