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

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

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tangent of-5x^2+x-2

tangent of

- 5 x^{2} + x - 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = - 5 x^{2} + x - 2 : \frac{d y}{d x} = - 10 x + 1

Compute the slope of

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

x = a_{0} : m = - 10 a_{0} + 1

Find the line with slope m=

- 10 a_{0} + 1

and passing through

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

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

\int_{0}^{9} \frac{1}{81 + x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 20 e^{t}, y (0) = - 4, y^{^{'}} (0) = 1

\int_{1}^{4} 6 e^{x} d x

f (x, y) = (x)^{2} + (y)^{4}

x \to 3 + lim (\frac{1}{∣ x - 3 ∣})

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