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

The tangent of 2x^2+2 is y=4a_{0}x-2a_{0}^2+2

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tangent of 2x^2+2

tangent of

2 x^{2} + 2

y = 4 a_{0} x - 2 a_{0}^{2} + 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 2 x^{2} + 2 : \frac{d y}{d x} = 4 x

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 = 4 a_{0}

Find the line with slope m=

4 a_{0}

and passing through

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

y = 4 a_{0} x - 2 a_{0}^{2} + 2

\frac{3}{s ^{2}}

\int \frac{1}{cos ( 4 x )} d x

x \to 4 lim (\frac{- 6}{4 - x})

\int x^{3} x^{2} + 41 d x

y = \frac{10}{( 10 - x ^{4} ) ^{\frac{3}{2}}}