What is the tangent of f(x)=4x^2+9x ?

The tangent of f(x)=4x^2+9x is y=(8a_{0}+9)x-4a_{0}^2

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tangent of f(x)=4x^2+9x

tangent of

f (x) = 4 x^{2} + 9 x

y = (8 a_{0} + 9) 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} + 9 a_{0})

Find the slope of

f (x) = 4 x^{2} + 9 x : \frac{df ( x )}{d x} = 8 x + 9

Compute the slope of

f (x) = 4 x^{2} + 9 x

x = a_{0} : m = 8 a_{0} + 9

Find the line with slope m=

8 a_{0} + 9

and passing through

(a_{0}, 4 a_{0}^{2} + 9 a_{0}) : y = (8 a_{0} + 9) x - 4 a_{0}^{2}

y = (8 a_{0} + 9) x - 4 a_{0}^{2}

\int \frac{6 t - 5}{t + 1} d t

f (x) = 5 x^{3}

(1 + x) d y = (y + x) d x

f (x) = x^{2} - x + 2, at x = 1

\int_{- π}^{0} 0 d x

What is the tangent of f(x)=4x^2+9x ?
The tangent of f(x)=4x^2+9x is y=(8a_{0}+9)x-4a_{0}^2