What is the tangent of (2x+5)(-x+2) ?

The tangent of (2x+5)(-x+2) is y=(-4a_{0}-1)x+2a_{0}^2+10

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tangent of (2x+5)(-x+2)

tangent of

(2 x + 5) (- x + 2)

y = (- 4 a_{0} - 1) x + 2 a_{0}^{2} + 10

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (2 a_{0} + 5) (- a_{0} + 2))

Find the slope of

y = (2 x + 5) (- x + 2) : \frac{d y}{d x} = - 4 x - 1

Compute the slope of

y = (2 x + 5) (- x + 2)

x = a_{0} : m = - 4 a_{0} - 1

Find the line with slope m=

- 4 a_{0} - 1

and passing through

(a_{0}, (2 a_{0} + 5) (- a_{0} + 2)) : y = (- 4 a_{0} - 1) x + 2 a_{0}^{2} + 10

y = (- 4 a_{0} - 1) x + 2 a_{0}^{2} + 10

\int \frac{4 x ^{3} - x}{6 x ^{2} - 2 x - 1} d x

x \to 0 lim (\frac{( 3 x ^{2} - 2 x )}{x})

\frac{d y}{d x} = x^{2} (1 + y^{2})

\int \frac{x ^{3}}{x ^{2} - 16} d x

x \to \infty lim (4 x^{4})

What is the tangent of (2x+5)(-x+2) ?
The tangent of (2x+5)(-x+2) is y=(-4a_{0}-1)x+2a_{0}^2+10