What is the tangent of 4x^5,\at (a=3) ?

The tangent of 4x^5,\at (a=3) is y=20a^4x-16a^5

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tangent of 4x^5,\at (a=3)

tangent of

4 x^{5}, at (a = 3)

y = 20 a^{4} x - 16 a^{5}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, 4 a^{5})

Find the slope of

y = 4 x^{5} : \frac{d y}{d x} = 20 x^{4}

Compute the slope of

y = 4 x^{5}

x = a : m = 20 a^{4}

Find the line with slope m=

20 a^{4}

and passing through

(a, 4 a^{5}) : y = 20 a^{4} x - 16 a^{5}

y = 20 a^{4} x - 16 a^{5}

6 x - 18, [2, 6]

\int - 9 csc^{2} (x) d x

g (x) = 11 x

g (x) = 9 - x^{2}

What is the tangent of 4x^5,\at (a=3) ?
The tangent of 4x^5,\at (a=3) is y=20a^4x-16a^5