What is the tangent of ax^3,\at x=-5 ?

The tangent of ax^3,\at x=-5 is y=75ax+250a

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tangent of ax^3,\at x=-5

tangent of

a x^{3}, at x = - 5

y = 75 a x + 250 a

Solution steps

Find the tangent point:

(- 5, - 125 a)

Find the slope of

y = a x^{3} : \frac{d y}{d x} = 3 a x^{2}

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 = 75 a

Find the line with slope m=

75 a

and passing through

(- 5, - 125 a) : y = 75 a x + 250 a

y = 75 a x + 250 a

What is the tangent of ax^3,\at x=-5 ?
The tangent of ax^3,\at x=-5 is y=75ax+250a