What is the tangent of 3x^2-4 ?

The tangent of 3x^2-4 is y=6a_{0}x-3a_{0}^2-4

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tangent of 3x^2-4

tangent of

3 x^{2} - 4

y = 6 a_{0} x - 3 a_{0}^{2} - 4

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0}^{2} - 4)

Find the slope of

y = 3 x^{2} - 4 : \frac{d y}{d x} = 6 x

Compute the slope of

y = 3 x^{2} - 4

x = a_{0} : m = 6 a_{0}

Find the line with slope m=

6 a_{0}

and passing through

(a_{0}, 3 a_{0}^{2} - 4) : y = 6 a_{0} x - 3 a_{0}^{2} - 4

y = 6 a_{0} x - 3 a_{0}^{2} - 4

y = x^{2}

y = 5

(53, 5)

f (x) = e^{3 x}

f (x) = x^{2} + 2