What is the tangent of f(x)=(25-0.075x)x,\at x=100 ?

The tangent of f(x)=(25-0.075x)x,\at x=100 is y=10x+750

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tangent of f(x)=(25-0.075x)x,\at x=100

tangent of

f (x) = (25 - 0.075 x) x, at x = 100

y = 10 x + 750

Solution steps

Find the tangent point:

(100, 1750)

Find the slope of

f (x) = (25 - 0.075 x) x : \frac{df ( x )}{d x} = - 0.15 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 = 10

Find the line with slope m=

10

and passing through

(100, 1750) : y = 10 x + 750

y = 10 x + 750

What is the tangent of f(x)=(25-0.075x)x,\at x=100 ?
The tangent of f(x)=(25-0.075x)x,\at x=100 is y=10x+750