What is the tangent of 5xsqrt(4-5x),\at x=-2 ?

The tangent of 5xsqrt(4-5x),\at x=-2 is y=(95)/(sqrt(14))x-10sqrt(14)+(95sqrt(2))/(sqrt(7))

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tangent of 5xsqrt(4-5x),\at x=-2

tangent of

5 x 4 - 5 x, at x = - 2

y = \frac{95}{14} x - 1014 + \frac{95 2}{7}

Solution steps

Find the tangent point:

(- 2, - 1014)

Find the slope of

y = 5 x 4 - 5 x : \frac{d y}{d x} = \frac{5 ( - 15 x + 8 )}{2 4 - 5 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{95}{14}

Find the line with slope m=

\frac{95}{14}

and passing through

(- 2, - 1014) : y = \frac{95}{14} x - 1014 + \frac{95 2}{7}

y = \frac{95}{14} x - 1014 + \frac{95 2}{7}

What is the tangent of 5xsqrt(4-5x),\at x=-2 ?
The tangent of 5xsqrt(4-5x),\at x=-2 is y=(95)/(sqrt(14))x-10sqrt(14)+(95sqrt(2))/(sqrt(7))