What is the tangent of f(x)=x+1-ln(x),\at x=0.5 ?

The tangent of f(x)=x+1-ln(x),\at x=0.5 is y=-x-ln(0.5)+2

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tangent of f(x)=x+1-ln(x),\at x=0.5

tangent of

f (x) = x + 1 - ln (x), at x = 0.5

y = - x - ln (0.5) + 2

Solution steps

Find the tangent point:

(0.5, - ln (0.5) + 1.5)

Find the slope of

f (x) = x + 1 - ln (x) : \frac{df ( x )}{d x} = - \frac{1}{x} + 1

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - 1

Find the line with slope m=

- 1

and passing through

(0.5, - ln (0.5) + 1.5) : y = - x - ln (0.5) + 2

y = - x - ln (0.5) + 2

What is the tangent of f(x)=x+1-ln(x),\at x=0.5 ?
The tangent of f(x)=x+1-ln(x),\at x=0.5 is y=-x-ln(0.5)+2