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

The tangent of 3x^2-5x is y=(6a_{0}-5)x-3a_{0}^2

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tangent of 3x^2-5x

tangent of

3 x^{2} - 5 x

y = (6 a_{0} - 5) x - 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 3 x^{2} - 5 x : \frac{d y}{d x} = 6 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 = 6 a_{0} - 5

Find the line with slope m=

6 a_{0} - 5

and passing through

(a_{0}, 3 a_{0}^{2} - 5 a_{0}) : y = (6 a_{0} - 5) x - 3 a_{0}^{2}

y = (6 a_{0} - 5) x - 3 a_{0}^{2}

\int \frac{e ^{4 x}}{e ^{4 x} + 3} d x

\frac{d}{d x} (cos (x^{2}) (2 x))

5 x^{2} - 3 x + 1

\frac{d}{d x} (3 \cdot 5^{x})

x \to 3 lim (2 x^{3} - 10 x - 8)

What is the tangent of 3x^2-5x ?
The tangent of 3x^2-5x is y=(6a_{0}-5)x-3a_{0}^2