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

The tangent of f(x)=sqrt(1+4x),\at x=2 is y= 2/3 x+5/3

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

tangent of

f (x) = 1 + 4 x, at x = 2

y = \frac{2}{3} x + \frac{5}{3}

Solution steps

Find the tangent point:

(2, 3)

Find the slope of

f (x) = 1 + 4 x : \frac{df ( x )}{d x} = \frac{2}{1 + 4 x}

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 = \frac{2}{3}

Find the line with slope m=

\frac{2}{3}

and passing through

(2, 3) : y = \frac{2}{3} x + \frac{5}{3}

y = \frac{2}{3} x + \frac{5}{3}

x \to c lim (x^{3} + 4 x^{2} - 3)

\int_{0}^{1} (3 + 2 x^{2}) d x

\frac{- x ^{2} - 7}{( x ^{2} - 7 ) ^{2}}

\int \frac{3 x ^{2}}{( 2 x ^{3} - 4 ) ^{2}} d x

\frac{2 s - 1}{s ^{2} - 6 s + 18}

What is the tangent of f(x)=sqrt(1+4x),\at x=2 ?
The tangent of f(x)=sqrt(1+4x),\at x=2 is y= 2/3 x+5/3