What is the tangent of f(x)=5x^2+7x ?

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

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tangent of f(x)=5x^2+7x

tangent of

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

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{d}{d x} (\frac{1}{2 x} - \frac{8}{3 x ^{2}})

\int (x^{3} - 2 x^{2})^{3} d x

x \to 0 - lim (e^{\frac{7}{x}})

\int \frac{1}{( x + a ) ^{2}} d x

\int sin (a x) sin (b x) d x

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