What is the tangent of f(x)=e^x(-4+7x+4x^2),\at x=0 ?

The tangent of f(x)=e^x(-4+7x+4x^2),\at x=0 is y=3x-4

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tangent of f(x)=e^x(-4+7x+4x^2),\at x=0

tangent of

f (x) = e^{x} (- 4 + 7 x + 4 x^{2}), at x = 0

y = 3 x - 4

Solution steps

Find the tangent point:

(0, - 4)

Find the slope of

f (x) = e^{x} (- 4 + 7 x + 4 x^{2}) : \frac{df ( x )}{d x} = 4 e^{x} x^{2} + 15 e^{x} x + 3 e^{x}

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

(0, - 4) : y = 3 x - 4

y = 3 x - 4

x \to a lim (ln (x - a))

y = \frac{6 ( x ^{4} - 3 )}{x ^{3}}

f (x) = \frac{x}{x + 6}

y = 6 x, y = 2 x - 6, y = 0

\frac{1}{x}, 1

What is the tangent of f(x)=e^x(-4+7x+4x^2),\at x=0 ?
The tangent of f(x)=e^x(-4+7x+4x^2),\at x=0 is y=3x-4