What is the tangent of f(x)=x+sqrt(x),\at x=4 ?

The tangent of f(x)=x+sqrt(x),\at x=4 is y= 5/4 x+1

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tangent of f(x)=x+sqrt(x),\at x=4

tangent of

f (x) = x + x, at x = 4

y = \frac{5}{4} x + 1

Solution steps

Find the tangent point:

(4, 6)

Find the slope of

f (x) = x + x : \frac{df ( x )}{d x} = 1 + \frac{1}{2 x}

Compute the slope of

f (x) = x + x

x = 4 : m = \frac{5}{4}

Find the line with slope m=

\frac{5}{4}

and passing through

(4, 6) : y = \frac{5}{4} x + 1

y = \frac{5}{4} x + 1

\int_{- 1}^{4} (x^{2} + 2 x - 1) d x

\frac{d}{d x} (- y x)

49 y^{^{''}} + 140 y^{^{'}} + 100 y = 0

x^{2} + 3

\int (3 - x^{2}) 2^{x} d x

What is the tangent of f(x)=x+sqrt(x),\at x=4 ?
The tangent of f(x)=x+sqrt(x),\at x=4 is y= 5/4 x+1