   Chapter 2.3, Problem 55E

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# Find equations of the tangent line and normal line to the curve at the given point. y = x + x ,    ( 1 , 2 )

To determine

To find:  Equation of tangent line and normal line to the curve y= x+x  at (1, 2)

Explanation

1) Concept:

Differentiate the given function to find the slope of tangent line and then find its negative reciprocal to find slope of normal line. Then using the given point and these two slopes, find the equation of tangent line and normal line.

2) Formula:

i. Power rule:  ddxxn=nxn-1

ii. Sum rule: ddxfx+gx=ddxfx+ddxg(x)

iii. Slope point formula:  y-y1=m  x- x1

3) Given:

y=x+x

4) Calculations:

Rewrite equation as,

y=x+x1/2

Differentiate y with respect to x,

y'=ddx(x+x1/2)

By using sum rule,

y'=ddx(x)+ddx(x1/2)

By using power rule,

y'=1+12(x-12)

y'=1+12x

Substituting x=1 we shall get value of derivative at x = 1.

y'|1=1+121=1+12=32

So this is the slope of tangent line

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