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

The tangent of f(x)=(5x-x^2)(5-x-x^2),\at x=1 is y=-3x+15

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

tangent of

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

y = - 3 x + 15

Solution steps

Find the tangent point:

(1, 12)

Find the slope of

f (x) = (5 x - x^{2}) (5 - x - x^{2}) : \frac{df ( x )}{d x} = 4 x^{3} - 12 x^{2} - 20 x + 25

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 = - 3

Find the line with slope m=

- 3

and passing through

(1, 12) : y = - 3 x + 15

y = - 3 x + 15

What is the tangent of f(x)=(5x-x^2)(5-x-x^2),\at x=1 ?
The tangent of f(x)=(5x-x^2)(5-x-x^2),\at x=1 is y=-3x+15