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

The tangent of y=(1+4x)^{3/2},\at x=2 is y=18x-9

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tangent of y=(1+4x)^{3/2},\at x=2

tangent of

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

y = 18 x - 9

Solution steps

Find the tangent point:

(2, 27)

Find the slope of

y = (1 + 4 x)^{\frac{3}{2}} : \frac{d y}{d x} = 6 (4 x + 1)^{\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 = 18

Find the line with slope m=

18

and passing through

(2, 27) : y = 18 x - 9

y = 18 x - 9

What is the tangent of y=(1+4x)^{3/2},\at x=2 ?
The tangent of y=(1+4x)^{3/2},\at x=2 is y=18x-9