What is the tangent of-3/2 x^2+5x+5 ?

The tangent of-3/2 x^2+5x+5 is y=(-3a_{0}+5)x+3/2 a_{0}^2+5

tangent of-3/2 x^2+5x+5

tangent of

- \frac{3}{2} x^{2} + 5 x + 5

y = (- 3 a_{0} + 5) x + \frac{3}{2} a_{0}^{2} + 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - \frac{3}{2} a_{0}^{2} + 5 a_{0} + 5)

Find the slope of

y = - \frac{3}{2} x^{2} + 5 x + 5 : \frac{d y}{d x} = - 3 x + 5

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 = - 3 a_{0} + 5

Find the line with slope m=

- 3 a_{0} + 5

and passing through

(a_{0}, - \frac{3}{2} a_{0}^{2} + 5 a_{0} + 5) : y = (- 3 a_{0} + 5) x + \frac{3}{2} a_{0}^{2} + 5

y = (- 3 a_{0} + 5) x + \frac{3}{2} a_{0}^{2} + 5

tan (2 x - x^{3})

\frac{\partial}{\partial x} (x^{3} y + 2 x y^{3})

\int (x + 2) e^{(x + 2)} d x

x \to 5 lim (\frac{x ^{2} + 1}{x + 1})

\int \frac{x}{36 x ^{2} + 9} d x

What is the tangent of-3/2 x^2+5x+5 ?
The tangent of-3/2 x^2+5x+5 is y=(-3a_{0}+5)x+3/2 a_{0}^2+5