What is the tangent of f(x)=5x^2+7x,\at-13 ?

The tangent of f(x)=5x^2+7x,\at-13 is y=(10a_{0}+7)x-5a_{0}^2

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tangent of f(x)=5x^2+7x,\at-13

tangent of

f (x) = 5 x^{2} + 7 x, at - 13

y = (10 a_{0} + 7) x - 5 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0}^{2} + 7 a_{0})

Find the slope of

f (x) = 5 x^{2} + 7 x : \frac{df ( x )}{d x} = 10 x + 7

Compute the slope of

f (x) = 5 x^{2} + 7 x

x = a_{0} : m = 10 a_{0} + 7

Find the line with slope m=

10 a_{0} + 7

and passing through

(a_{0}, 5 a_{0}^{2} + 7 a_{0}) : y = (10 a_{0} + 7) x - 5 a_{0}^{2}

y = (10 a_{0} + 7) x - 5 a_{0}^{2}

\frac{\partial}{\partial x} ((x - 1)^{2} e^{x})

\frac{d}{d x} (\frac{132}{x ^{13}})

\int_{0}^{\infty} 3 x e^{- 3 x} d x

\int \frac{x ^{2} - 1}{x ^{3} - 3 x} d x

\int \frac{x + 6}{x} d x

What is the tangent of f(x)=5x^2+7x,\at-13 ?
The tangent of f(x)=5x^2+7x,\at-13 is y=(10a_{0}+7)x-5a_{0}^2