What is the tangent of f(x)=4x^2+7x ?

The tangent of f(x)=4x^2+7x is y=(8a_{0}+7)x-4a_{0}^2

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tangent of f(x)=4x^2+7x

tangent of

f (x) = 4 x^{2} + 7 x

y = (8 a_{0} + 7) x - 4 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0}^{2} + 7 a_{0})

Find the slope of

f (x) = 4 x^{2} + 7 x : \frac{df ( x )}{d x} = 8 x + 7

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 = 8 a_{0} + 7

Find the line with slope m=

8 a_{0} + 7

and passing through

(a_{0}, 4 a_{0}^{2} + 7 a_{0}) : y = (8 a_{0} + 7) x - 4 a_{0}^{2}

y = (8 a_{0} + 7) x - 4 a_{0}^{2}

\int \frac{1}{u ^{2} - 4} d u

\frac{d}{d θ} (θ)

\int sin (7 x) cos (7 x) d x

\frac{\partial}{\partial x} (\frac{x - y}{2 x y + 5})

(sin (x))^{x}

What is the tangent of f(x)=4x^2+7x ?
The tangent of f(x)=4x^2+7x is y=(8a_{0}+7)x-4a_{0}^2