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

The tangent of f(x)=5xsqrt(5-4x),\at x=-2 is y=(85)/(sqrt(13))x-10sqrt(13)+(170)/(sqrt(13))

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

tangent of

f (x) = 5 x 5 - 4 x, at x = - 2

y = \frac{85}{13} x - 1013 + \frac{170}{13}

Solution steps

Find the tangent point:

(- 2, - 1013)

Find the slope of

f (x) = 5 x 5 - 4 x : \frac{df ( x )}{d x} = \frac{5 ( - 6 x + 5 )}{5 - 4 x}

Compute the slope of

f (x) = 5 x 5 - 4 x

x = - 2 : m = \frac{85}{13}

Find the line with slope m=

\frac{85}{13}

and passing through

(- 2, - 1013) : y = \frac{85}{13} x - 1013 + \frac{170}{13}

y = \frac{85}{13} x - 1013 + \frac{170}{13}

\frac{x}{x - 3}

x \to 0 + lim (x e^{- \frac{1}{x}})

\frac{d}{d x} (2 e^{x})

\int \frac{x ^{2} - 6}{6 x} d x

\frac{\partial}{\partial s} (t + 3 t^{3} sin (s))

What is the tangent of f(x)=5xsqrt(5-4x),\at x=-2 ?
The tangent of f(x)=5xsqrt(5-4x),\at x=-2 is y=(85)/(sqrt(13))x-10sqrt(13)+(170)/(sqrt(13))