What is the tangent of f(x)=2xsqrt(3-4x),\at x=-1 ?

The tangent of f(x)=2xsqrt(3-4x),\at x=-1 is y=(18)/(sqrt(7))x-2sqrt(7)+(18)/(sqrt(7))

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tangent of f(x)=2xsqrt(3-4x),\at x=-1

tangent of

f (x) = 2 x 3 - 4 x, at x = - 1

y = \frac{18}{7} x - 27 + \frac{18}{7}

Solution steps

Find the tangent point:

(- 1, - 27)

Find the slope of

f (x) = 2 x 3 - 4 x : \frac{df ( x )}{d x} = \frac{2 ( - 6 x + 3 )}{3 - 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{18}{7}

Find the line with slope m=

\frac{18}{7}

and passing through

(- 1, - 27) : y = \frac{18}{7} x - 27 + \frac{18}{7}

y = \frac{18}{7} x - 27 + \frac{18}{7}

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What is the tangent of f(x)=2xsqrt(3-4x),\at x=-1 ?
The tangent of f(x)=2xsqrt(3-4x),\at x=-1 is y=(18)/(sqrt(7))x-2sqrt(7)+(18)/(sqrt(7))