What is the tangent of f(x)=5x-x^2,(1,4) ?

The tangent of f(x)=5x-x^2,(1,4) is y=3x+1

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tangent of f(x)=5x-x^2,(1,4)

tangent of

f (x) = 5 x - x^{2}, (1, 4)

y = 3 x + 1

Solution steps

Find the slope of

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

Compute the slope of

f (x) = 5 x - x^{2}

(1, 4) : m = 3

Find the line with slope m=

3

and passing through

(1, 4) : y = 3 x + 1

y = 3 x + 1

(1 + x) d y - y d x = 0

x \to \infty lim (6^{x})

x \to 0 - lim (f (x))

f (x) = - 3 e^{x + 1}

f (x) = 8 x - x^{2}

What is the tangent of f(x)=5x-x^2,(1,4) ?
The tangent of f(x)=5x-x^2,(1,4) is y=3x+1