What is the tangent of f(x)=2sqrt(x)+1,\at x= 1/4 ?

The tangent of f(x)=2sqrt(x)+1,\at x= 1/4 is y=2x+3/2

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tangent of f(x)=2sqrt(x)+1,\at x= 1/4

tangent of

f (x) = 2 x + 1, at x = \frac{1}{4}

y = 2 x + \frac{3}{2}

Solution steps

Find the tangent point:

(\frac{1}{4}, 2)

Find the slope of

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

Compute the slope of

f (x) = 2 x + 1

x = \frac{1}{4} : m = 2

Find the line with slope m=

2

and passing through

(\frac{1}{4}, 2) : y = 2 x + \frac{3}{2}

y = 2 x + \frac{3}{2}

\int 4 e^{\frac{x}{2}} d x

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

\frac{d}{d x} (\frac{x ^{e^{x}}}{1 + x ^{2}})

\frac{d}{d x} (sin (e^{x}))

\frac{d}{d θ} (e^{2 θ})

What is the tangent of f(x)=2sqrt(x)+1,\at x= 1/4 ?
The tangent of f(x)=2sqrt(x)+1,\at x= 1/4 is y=2x+3/2