What is the tangent of y=9x^{5/2}-7x^{3/2},\at x=4 ?

The tangent of y=9x^{5/2}-7x^{3/2},\at x=4 is y=159x-404

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tangent of y=9x^{5/2}-7x^{3/2},\at x=4

tangent of

y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}, at x = 4

y = 159 x - 404

Solution steps

Find the tangent point:

(4, 232)

Find the slope of

y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}} : \frac{d y}{d x} = \frac{45 x ^{\frac{3}{2}} - 21 x ^{\frac{1}{2}}}{2}

Compute the slope of

y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}

x = 4 : m = 159

Find the line with slope m=

159

and passing through

(4, 232) : y = 159 x - 404

y = 159 x - 404

\frac{d y}{d x} - 2 (x + 1)^{3} = \frac{4}{( x + 1 )} y

f (x) = arctan (\frac{π}{x})

y^{^{'}} = 6 y^{2} sin (x)

\int \frac{1}{( 9 x - 1 ) ^{2}} d x

\int_{- 14}^{7} (7 e^{x}) d x

What is the tangent of y=9x^{5/2}-7x^{3/2},\at x=4 ?
The tangent of y=9x^{5/2}-7x^{3/2},\at x=4 is y=159x-404