What is the tangent of f(x)=(10x-4)^{1/2},\at x=2 ?

The tangent of f(x)=(10x-4)^{1/2},\at x=2 is y= 5/4 x+3/2

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tangent of f(x)=(10x-4)^{1/2},\at x=2

tangent of

f (x) = (10 x - 4)^{\frac{1}{2}}, at x = 2

y = \frac{5}{4} x + \frac{3}{2}

Solution steps

Find the tangent point:

(2, 4)

Find the slope of

f (x) = (10 x - 4)^{\frac{1}{2}} : \frac{df ( x )}{d x} = \frac{5}{( 10 x - 4 ) ^{\frac{1}{2}}}

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{5}{4}

Find the line with slope m=

\frac{5}{4}

and passing through

(2, 4) : y = \frac{5}{4} x + \frac{3}{2}

y = \frac{5}{4} x + \frac{3}{2}

What is the tangent of f(x)=(10x-4)^{1/2},\at x=2 ?
The tangent of f(x)=(10x-4)^{1/2},\at x=2 is y= 5/4 x+3/2