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Popular >

tangent of 5x^2+8x-8

Solution

tangent of

5 x^{2} + 8 x - 8

Solution

y = (10 a_{0} + 8) x - 5 a_{0}^{2} - 8

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0}^{2} + 8 a_{0} - 8)

Find the slope of

y = 5 x^{2} + 8 x - 8 : \frac{d y}{d x} = 10 x + 8

Compute the slope of

y = 5 x^{2} + 8 x - 8

at

x = a_{0} : m = 10 a_{0} + 8

Find the line with slope m=

10 a_{0} + 8

and passing through

(a_{0}, 5 a_{0}^{2} + 8 a_{0} - 8) : y = (10 a_{0} + 8) x - 5 a_{0}^{2} - 8

y = (10 a_{0} + 8) x - 5 a_{0}^{2} - 8

Popular Examples

d/(du)(sqrt(u))

\frac{d}{d u} (u)

derivative of (6x-1(5x-2)^{-1})

\frac{d}{d x} ((6 x - 1) (5 x - 2)^{- 1})

derivative of 2(x-1^2)

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

y^{''}+4y^'+5y=-10x+3e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + 3 e^{- x}

limit as x approaches 3 of sqrt(x-2)

x \to 3 lim (x - 2)

Frequently Asked Questions (FAQ)

What is the tangent of 5x^2+8x-8 ?
The tangent of 5x^2+8x-8 is y=(10a_{0}+8)x-5a_{0}^2-8